Resuming day two on 255-4, Khawaja (180) and Green (114) piled more runs on to frustrate the hosts with a fifth-wicket partnership of 208, while Australia's tail also wagged.
Ravichandran Ashwin produced figures of 6-91 to stop the tourists from doing even more damage, before Rohit Sharma (17 not out) and Shubman Gill (18 not out) made a promising start to India's reply, ending the day 36-0, still trailing by 444 runs.
Khawaja and Green continued their impressive partnership from day one, with the latter hitting his maiden Test century before a sweep attempt saw him glove one from Ashwin to Srikar Bharat.
Ashwin soon found his groove as he removed Alex Carey for a duck and Mitchell Starc for six, while Khawaja was finally out lbw after a review off the first ball after the tea interval from Axar Patel.
Lyon (34) and Murphy (41) were in the mood to play some shots though, and had plenty of joy as they struck 11 fours between them in a ninth-wicket partnership of 70, before both fell to Ashwin.
The surface in Ahmedabad has been kinder to batters than others in the series, and Rohit and Gill had few problems seeing off Australia's bowling attack in their 10 overs before close.
Gill launched the first six of the match in the final over of the day off Lyon, but India still have plenty to do to get close to the Baggy Green's first innings total.
Khawaja shows patience is a virtue
Khawaja had already reached three figures on day one, but continued his impressively mature innings alongside Green on Friday, lasting 422 balls in all, the most faced of any Australian batter in an innings in India in Test history.
After the day ended, Green said: "Ussie helped me so much out there. It is really special."
Ashwin overtakes Kumble in Australia battles
It must be a strange feeling for a bowler to post numbers as impressive as 6-91 but see the opponents still score almost 500 runs.
It may be consolation for Ashwin that his 113 wickets in total means he has surpassed Anil Kumble (111 wickets) and equalled Lyon to become the joint-leading wicket-taker in the Border Gavaskar Trophy.
The tourists, who trail the four-Test series 1-0 after an innings defeat in Nagpur, managed to reach 263 in Delhi after opener Khawaja made 81 and Handscomb 72 not out.
India skipper Rohit Sharma (13) and KL Rahul (4) guided India to 21-0 at the close of play on Friday to leave them trailing by 242 in the first innings.
Khawaja put on a 50-wicket stand with David Warner (15) for the opening wicket, but Ravichandran Ashwin – who finished with figures of 3-57 – dismissed Marnus Labuschagne (18) and Steve Smith (0) in the space of three balls.
Warner was struck on the helmet and elbow in separate incidents prior to being dismissed cheaply and was later unable to field.
The returning Travis Head could only add 12 runs before Handscomb joined Khawaja to share 59 for the fifth wicket, but the latter was caught by Rahul in the covers, shortly before Alex Carey went for a duck.
Australia were 168-6 at that point, though Handscomb put on another 59 with skipper Pat Cummins, who was sent packing lbw for 33 by Ravindra Jadeja, who also removed Todd Murphy (0) in the same over.
Mohammed Shami returned to remove Nathan Lyon and debutant Matthew Kuhnemann, seeing him finish with figures of 4-60, as Australia were sent packing inside 79 overs.
India managed nine overs in response, with Cummins, Kuhnemann and Lyon unable to remove Rohit and Rahul, who will resume play on Saturday.
Ravindra reaches milestone figure
Jadeja took three wickets in 21 overs to become only the fourth Indian, after Anil Kumble, Kapil Dev and Ravichandran Ashwin, to record 2,500 Test runs and 250 wickets in the format.
It leaves India in a good position to push on and record a third straight Test victory over Australia for the first time since 2013, when winning four in a row against their Border–Gavaskar Trophy rivals.
Khawaja keeps things interesting
After his double failure in the first Test, Khawaja was bold at the start of play in Delhi and his 81 runs came off 125 balls, though he looked devastated when Rahul's leaping one-handed snare denied him a century.
It could have been better for Khawaja and Australia, but it may yet be enough in the grand scheme of things.
"We actually don't know what a good score is on this wicket," the left-handed batter told BT Sport. "If we bowl well, then 260 will be a competitive score.
"There is something in the pitch and plates were moving already when we were batting. Tomorrow will tell the tale of where this game is going."
Australia were 475-4 at stumps after play was interrupted by light rain at drinks in the final session with Khawaja unbeaten on 195* alongside Matt Renshaw (5*).
The hosts were utterly dominant, beating the Proteas into submission, with only two wickets falling across 84 overs bowled for the day. However, the issue of time remaining in the Test looms large after more delays on day two, with grim weather forecast for Sydney in the coming days.
Khawaja had resumed alongside Smith with Australia 148-2 after only 47 overs were bowled on day one due to a combination of bad light and rain.
After an early rain delay, the 36-year-old left-handed opening batsman led from the front, bringing up his 13th Test century late in the opening session with two off Kagiso Rabada.
Khawaja celebrated his third straight SCG hundred with an air-punch and a little jig. Smith brought up his half-century shortly after.
South Africa skipper Dean Elgar demonstrably discarded the old ball when the Proteas took the new ball shortly before lunch, but it led to few opportunities for the tourists.
Smith went on to bring up his 30th Test century, surpassing the great Sir Donald Bradman, pulled to the backward square leg boundary from Anrich Nortje to reach triple figures.
But the vice-captain was dismissed caught and behind by Keshav Maharaj for 104 in the next over, ending their 209-run third-wicket stand. That marked the pair's 10th century partnership from 33 innings.
Travis Head kept the game moving with aggressive stroke play, blasting eight fours and one six before being caught by sub fielder Rassie van der Dussen at deep square off the tiring Rabada.
Renshaw, who tested positive to COVID on day one and had to keep his distance from team-mates, batted late in the day before stumps was called.
Patient Khawaja bats through
Khawaja finished the day unbeaten on 195, having faced 368 deliveries with 19 fours and one six, batting through the opening two days, albeit amid numerous delays. The Queenslander's 195* is his highest Test score and he will be chasing a maiden Test double hundred on Friday.
Maharaj breaks duck
Proteas left-arm orthodox spinner Maharaj had endured a lean series prior to claiming Smith's wicket, which was his first in the three Tests. That dismissal ended Maharaj's dire record of 0-247 from 66.5 overs in the series.
Khawaja, who returned to the Test side during the Ashes after more than two years outside the team, was named in Australia's squad for next month's Pakistan Test series.
The 35-year-old admitted he was sad for "the person" when Langer resigned as Australia head coach amid a messy exit with talk of a player revolt.
Langer spent almost four years in the head coaching role but resigned on Saturday, rejecting a six-month contract extension.
The 51-year-old's exit comes after leading Australia to a 4-0 Ashes triumph and a stunning T20 World Cup victory which has raised eyebrows, yet there have been rumblings of internal issues.
"I just came back in the team two months ago. I've been a little bit out of it, a little bit disconnected, but there's obviously a lot of ex-players coming and talking about the playing group," Khawaja told reporters on Tuesday.
"At some stage, one of the captains, probably Finchy or Patty, will probably have to stand up and answer some questions just to get rid of all the speculation that's going around. To just put an end to it all."
Khawaja said Langer had tried to take on player feedback and insisted "always got along with him".
But several key members of the Australian side, including Cummins, failed to publicly back Langer for a contract extension in the lead-up to Saturday's announcement.
"It's part of speculation which I don't think is really healthy. I just don't want to add to it," Cummins said on Thursday when asked about a contract renewal for Langer.
"That's Cricket Australia's job. It's not my job. I've really loved my time working with JL and we've had an evaluation process. I've been part of that, a lot of other players and staff have been part of that.
"Just like when we get evaluated. I've got huge respect for JL, really like working with him. But it's not my call."
The opener said he had completed "a long journey" by finally making it to three figures on what is his third tour of India in the long format.
Australia amassed 255-4, with Khawaja 104 not out at stumps, reaching his ton with a boundary from the first ball of the day's final over.
A nine-wicket victory for Australia in the third Test last week has fuelled hope they could complete a fightback from 2-0 behind to draw this series, and this start boded well.
While it was Khawaja's day, others helped the score along, with Travis Head making a brisk 32 at the top of the innings and captain Steve Smith adding a hardy 38 from 135 balls before falling to an inside edge off Ravindra Jadeja.
Mohammed Shami bowled Marnus Labuschagne (3) and Peter Handscomb (17), but Cameron Green cracked a rapid 49no containing eight fours as he kept Khawaja company late in the day.
Khawaja got to 99 with a single from the final ball of the penultimate over, making it a nerve-jangling end to day one as he retained the strike to face Shami.
The 36-year-old left-hander held his nerve, clipping away a leg-side four to make it a day for him and Australia to savour. It took him 246 deliveries to get there, and Khawaja will look to bat on deep into Friday to pile pressure on India.
Comeback on the cards?
After day one, Australia will be fancying their task in this match. They are seeking back-to-back men's Test wins against India for the first time since December 2014, and the last time they had consecutive wins in a series in India was in December 1969. India have not lost more than one game in a men's Test series on home soil since losing 2-1 to England in November-December 2012. The hosts can't lose this series, of course, but a draw might feel like a defeat given they won the opening two Tests.
Classy Khawaja
Six of Khawaja's 14 Test tons have come since the start of 2022, underlining what a sensational late-career revival he is enjoying. This was his first Test century against India at any ground, with his previous highest score having been the 81 he made last month in Delhi. In an end-of-day interview, he recalled being a drinks carrier on his first two tours of India, but this time he is making his presence felt.
After drawing last week's opening Test in Rawalpindi, it was Australia who laid down an early marker on Saturday as they reached stumps on 251-3.
The in-form Khawaja batted all day as he made an unbeaten 127, while Steve Smith was also on course for three figures before being caught by Faheem Ashraf off the bowling of Hasan Ali for 72 just before the close.
Khawaja profited from what he described as "pretty negative" bowling from the hosts to hit 13 fours and one six in a classy knock.
David Warner went for 36 and Marnus Labuschagne was run out on a duck, but Khawaja's batting ensured even the late loss of Smith did not hamper the tourists too much.
Nathan Lyon will resume alongside Khawaja on Sunday as Pakistan look to make inroads after a frustrating opening day.
"It would have been nice to have Smith there at the end," Khawaja said. "We've still got plenty of batting to come.
"The wicket was pretty nice today and is going to get worse, and it's feeling like it'll break up in the back end of the match.
"They bowled pretty negative and we were not going to give them free wickets. It would have been nice to get a hundred both in Rawalpindi and here but I'll take this one."
Khawaja goes one better
After falling three short of a century in Rawalpindi last week, the Islamabad-born Khawaja was not to be denied an 11th Test century on Saturday.
He has now logged two centuries and five half-centuries across eight Test innings against his country of birth.
Pakistan falter
Babar Azam's tactics after tea must be questioned, though Hasan did find a breakthrough when ending a 159-run partnership late on to give Pakistan a platform to build on.
Pakistan have only suffered two defeats at the National Stadium in 44 Tests and will need some quick wickets with the new ball in Sunday's morning session.
Responding to Pakistan's first innings' 476-4 declared and resuming on five without loss, Khawaja's 97, along with half-centuries from David Warner (68) and Marnus Labuschagne (69 not out), took the tourists to 271-2 - trailing by 205 runs when bad light stopped play.
It means Australia, playing with heavy hearts following the sudden passing of legendary leg-spinner Shane Warne on Friday, are in an excellent position to at least claim a draw.
The Islamabad-born Khawaja and Warner laid the foundations, combining for a stand of 156, the second-highest opening partnership in Test history in Rawalpindi.
Both Khawaja and Warner played in attacking fashion, the former's half-century coming off just 67 balls. Warner's came in 86, but he was undone when he attempted to go square through the off side and missed a Sajid Khan delivery that careered into middle stump.
His exit did not open the floodgates as Pakistan might have hoped, but they did at least prevent Khawaja from recording an 11th Test hundred.
Khawaja contributed to his own downfall as he got a reverse sweep all wrong, gloving Nauman Ali to Imam-ul-Haq at foward short-leg, with Aleem Dar forced to overturn his original not out decision following a review.
Yet, with Labuschange and Steve Smith (24 not out) surviving until the fading light forced the players off, Australia have two batters who are among the most difficult in world cricket to dislodge set at the crease, a sign that is, for Pakistan, as ominous as the gloom that stopped proceedings.
Khawaja and Warner narrowly miss out on history
Only Mark Taylor and Michael Slater (176) have linked up for a higher first-wicket stand than Khawaja and Warner in Rawalpindi, that duo excelling in October 1994 in a match that ultimately ended in a draw. The same result looks likely again here after Khawaja and Warner narrowly missed out on surpassing their compatriots.
Labuschagne to let loose?
Pakistan will have painful memories of their previous two encounters against Labuschagne, which saw him score 185 at Brisbane and then 162 at Adelaide in 2019. He looks in the kind of form to deliver another massive score.
The opener carried the bat through sweltering conditions at Narendra Modi Stadium with a resolute knock to put the visitors on track for their best total of the series.
His efforts halted a long wait for an Australian to reach triple figures in a Test innings in the country, with interim captain Steve Smith the last to achieve it in 2017.
For Khawaja, his performance was a fitting pay-off for previous visits to the country where he failed to get on the pitch, offering a satisfying start to the final game in Ahmedabad.
"There was a lot of emotion in that," he said. "I have been to India on two tours before this, and carried the drinks in all eight Test matches. It was a long journey.
"To finally get a hundred in India, as an Australian, that's what you want to do, that's what you want to tick off. It's very special.
"It was such a nice wicket; I just didn't want to give my wicket away. It was a mental battle more than anything. You need to put your ego away. It was a battle all day."
Australia are looking to tie the Border-Gavaskar Trophy after they claimed a nine-wicket victory in the third Test earlier this month, following losses in the first two games.
Draws in the first two Tests set up a winner-take-all contest in Lahore, where the surface appears to have plenty in it for the bowlers to ensure a result this time around.
Shaheen's blistering start suggested as much, as the Pakistan seamer removed David Warner and Marnus Labuschagne in the space of three deliveries to leave Australia reeling on 8-2.
But Khawaja, born in Pakistan, once again excelled with the bat, he and Steve Smith leading the Australia response to help them fight back to reach 232-5 at stumps. Khawaja was denied a second century of the series, as a stunning one-handed catch at slip from Babar Azam saw him out for 91.
Bowlers have consistently had to work hard for wickets in an attritional series but when Shaheen had Warner (7) trapped lbw and Labuschagne edged a poor shot behind to fall for a duck, Pakistan had hope of blitzing their way through a frequently steadfast Australia batting order.
Any such prospect was extinguished by the partnership of Khawaja and Smith (59), the latter recording his third successive half-century as they put on 138 for the third wicket.
But Naseem had Smith trapped in front to end his hopes of converting his fifty into a hundred and Khawaja was then denied three figures by Sajid Khan and the brilliance of Babar.
An excellent length delivery from Naseem removed Travis Head for 26, though Cameron Green and Alex Carey's unbroken partnership of 26 from 42 balls gave Australia reason for hope at the close.
Khawaja shows his class again
After falling three short of a hometown century at Rawalpindi in the opener, Khawaja - having hit a brilliant 160 in the second Test - again fell in the 90s here, but his consistency since returning to Test set-up in January has been remarkable. He has now scored at least 90 in five of his last eight innings.
Smith closing on 8,000
Smith did not review the delivery that ended his innings, but there must have been a great deal of temptation to do so given his dismissal left him just seven runs shy of 8,000 in the longest format.
Khawaja, 33, was dropped from the Test team during last year's Ashes, while his last ODI was also in 2019.
Marsh, 36, has been out of international action since mid-2019 and was also left off a 20-player list named on Thursday.
"As Mitch Marsh and Matthew Wade have proven there are always plenty of opportunities for those who have missed out to be reselected by performing consistently at domestic level; and importantly to make the most of any opportunity that comes their way at international level," Australia national selector Trevor Hohns said in a statement.
"As is always the case there are unlucky omissions but, however, because you are not on the list does not mean you cannot be selected to represent Australia."
Marnus Labuschagne, Joe Burns, Matthew Wade, Mitchell Marsh, Kane Richardson and Ashton Agar were called up to the nationally contracted list.
It continues Labuschagne's incredible rise, with the right-hander averaging 63.43 in 14 Tests and 50.83 in seven ODIs.
"We feel all deserve their inclusion recognising the performances of those players in the past 12 months and, as importantly, what they can offer in the next 12 months," Hohns said.
"Marnus' rise has been meteoric and well documented, Joe has been a good Test match player, Ashton Agar’s form in T20 internationals has been exceptional, while Kane Richardson has been outstanding in the 20-over and one-day games.
"Matthew Wade's summer showed he is not only a tough but a good Test player for us. His form extended into white-ball cricket late in the summer, earning him well-deserved call-ups to the one-day and T20 Australian squads.
"After missing the list last year Mitch Marsh's recent form showed he has a lot of international cricket ahead of him as a batting all-rounder. Mitch proved this with his man-of-the-match performance against New Zealand at the SCG in the last game Australia played and a five-wicket haul in the last Test match he played on the Ashes tour."
Cricket Australia contracted player list: Ashton Agar, Joe Burns, Alex Carey, Pat Cummins, Aaron Finch, Josh Hazlewood, Travis Head, Marnus Labuschagne, Nathan Lyon, Mitchell Marsh, Glenn Maxwell, Tim Paine, James Pattinson, Jhye Richardson, Kane Richardson, Steve Smith, Mitchell Starc, Matthew Wade, David Warner, Adam Zampa.
England Test captain Ben Stokes retired from ODIs this week, stating it was "unsustainable" for him to play for his country in the longest format, plus Twenty20s and the 50-over game.
Stokes warned that players cannot be treated like "cars" and keep clocking up mileage with such a hectic schedule.
Australia batter Khawaja is not convinced there is a long-term future for ODI cricket.
He said: "My own personal opinion – I know a few of the guys are very similar – you've got Test cricket, which is the pinnacle, you've got T20 cricket, which obviously has leagues around the world, great entertainment, everyone loves it, and then there's one-day cricket.
"I feel like that's probably the third-ranked out of all of them. I think personally one-day cricket is dying a slow death... there's still the World Cup, which I think is really fun and it's enjoyable to watch, but other than that, even myself personally, I'm probably not into one-day cricket as much either."
Khawaja believes it is a big ask for players to play in all formats.
"Not impossible, very tough," Khawaja said, quoted by the Australian Associated Press. "So much travelling. If you're playing all three forms of the game, you're not at home at all really.
"And then the demands on your body, mentally, physically and a lot of the guys might be playing also the IPL.
"There's a lot of cricket going on. Yes, you get to pick and choose, I guess, in certain respects what you want to play, but it can be very tough at the moment."
While Khawaja does not see a bright ODI future, he is not concerned about Test cricket.
"The majority of people I talk to still love Test cricket," he said. "It's my favourite format. [I] think Test cricket still has a very strong presence so don't really see that going anywhere."
Current England coach and selector Silverwood has come under scrutiny after defeat to Australia, with the tourists already down and out at 3-0 in the series with two Tests left to play.
The former India and South Africa coach Kirsten, who led both of those sides to the top of the red-ball rankings, has twice been linked with the England role and is likely to be a favoured candidate again should Silverwood depart.
Former Proteas opener Kirsten expressed his interest in the job but insisted he would only take charge of the red-ball side if Eoin Morgan's dominant white-ball team would be coached by someone else.
"Listen, it [the England job] is always a consideration because it's a tremendous honour," Kirsten told iNews.
"I've walked this journey twice now [when England recruited new coaches in 2015 and 2019] and I've always made it clear that I would never commit to doing all formats.
"And when international cricket boards get their head around the fact that they need to split coaching roles, then it becomes a consideration.
"Working with a Test side, or working with an ODI side is great. Listen, the England ODI side is set up, you're the best ODI side in the world at the moment.
"It's a project that has been well thought-out. You've got consistency in the players that have been picked. Your Test side has battled for a while, but it would be a really lovely project to get that going."
Indeed, the 54-year-old was a frontrunner to replace Trevor Bayliss when he parted ways with England in 2019 before Silverwood was eventually appointed as the Australian's successor.
Kirsten, who has previously built formidable Test sides with both India and South Africa, could be sensing another great rebuild should Silverwood be given his marching orders in the wake of another Ashes hammering.
"Interestingly, when I finished with India and I joined South Africa, we just looked at it and said 'our priority has to be Test match cricket'," he added. "I actually said to the CEO of Cricket South Africa that I was happy to just do the Test side because I felt it should be the number one side in the world.
"It had all the credentials to do that. The issue is that the different formats have the potential to cannibalise teams. You focus too much attention on one format and the other format takes the hit.
"It's not easy to get everything right. Look at Australia, they're now using a lot of players across the different formats.
"It [England] is an interesting one. I think it's a great project for someone to come in and take that Test side on. There's a lot that needs to be put in place to build this Test team out."
Kirsten is already on the ECB's payroll, having worked with the Welsh Fire in the inaugural Hundred competition, where conversations with some key figures surprised him as to the uncertainties and deficiencies within the English game.
"When I was over there I asked a number of coaches and players who their top six would be for the England Test side – and I never got the same answer from anyone," he continued.
"That's a good illustration of the issue you have. If you don't know what your top six is, or really have no idea of the best six batsmen in the country, then how can build consistency around guys who are going to come in and, when needed, make a play?"
India face Australia, who host the upcoming World Cup as reigning champions, in a three-match T20I series starting on Tuesday.
With Rohit rested for India's final Asia Cup match, Kohli filled in at the top of the order and plundered an unbeaten 122 from 61 balls to help seal an emphatic 101-run win over Afghanistan.
Kohli's knock is the highest score by an Indian player in men's T20Is, overtaking Rohit's 118 against Sri Lanka in December 2017, while it also ended his 1,020-day wait for an international century.
Ahead of the first match in Mohali, Rohit told a press conference: "It's always nice to have options available to you. It is very important when you go in a tournament like a World Cup.
"You want the flexibility. We only talk about it, but this is actually what it means. You want your players to be in their best shape, batting in any position and so on.
"For us, when we try and do something new, it doesn't mean that is permanent. We understand the quality of all the players and what they bring to us. We do understand that, but it is an option for us.
"We will keep that in mind that since we haven't taken a third opener, [Kohli] can obviously open. He opens for his franchise and has done really well. We saw that in the last match, and we are quite happy with what we saw. I don't think we will experiment for that position a lot."
Rahul struck 62 in India's win over Afghanistan, though he has not scored a century in the shortest format since 2018.
However, he remains Rohit's first pick.
"KL Rahul will play the World Cup, and open," Rohit affirmed. "His performances for India tend to go unnoticed. He is a very important player for India. If you look at his record over the last two, three years, it is very good.
"I don't think it is right to not consider one performance because someone else has performed. There is no confusion. We are very clear about what KL brings to us.
"He is a very, very important and quality player and a match-winner as well. His presence at the top is very, very crucial for us."
Six people were ejected from the iconic Sydney venue on day four after India paceman Mohammed Siraj reported he was the target of abuse while he was fielding on the boundary.
The India team staff also reported alleged racial abuse of Jasprit Bumrah and Siraj on Saturday.
Play was halted for around 10 minutes on Sunday, with umpires and security guards holding discussions before the spectators were removed by New South Wales Police.
The International Cricket Council (ICC) strongly condemned the reported incidents and offered Cricket Australia (CA) all necessary support with an investigation.
India captain Kohli, who is back in his homeland as his wife is expecting a baby, said action must be taken as soon as possible.
He tweeted: "Racial abuse is absolutely unacceptable. Having gone through many incidents of really pathetic things said on the boundary Iines, this is the absolute peak of rowdy behaviour. It's sad to see this happen on the field.
"The incident needs to be looked at with absolute urgency and seriousness and strict action against the offenders should set things straight for once."
CA head of integrity and security Sean Carroll earlier said in a statement: "Cricket Australia condemns in the strongest terms possible all discriminatory behaviour.
"If you engage in racist abuse, you are not welcome in Australian cricket. CA is awaiting the outcome of the International Cricket Council's investigation into the matter reported at the SCG on Saturday.
"Once those responsible are identified, CA will take the strongest measures possible under our anti-harassment code, including lengthy bans, further sanctions and referral to NSW Police.
"As series hosts, we unreservedly apologise to our friends in the Indian cricket team and assure them we will prosecute the matter to its fullest extent."
India spinner Ravichandran Ashwin claimed India have experienced abuse on previous tours of Australia.
"This is my fourth tour to Australia and in Sydney, especially, we have had a few experiences even in the past," he said.
"I think one or two times even the players have reacted and got into trouble in the past, and that's not because of the player, it is actually because of the way the crowd has been speaking, especially the people close to the boundary edge.
"They have been quite nasty, they have been hurling abuse as well, but this is the time they have gone one step ahead and used racial abuse.
"There was an official complaint lodged yesterday, and the umpires also mentioned it to us that we must bring it to their notice as soon as it happens, on the field, and then they will be able to take action.
"It is definitely not acceptable in this day and age. We have seen a lot, right? We have evolved as a society. This must be definitely dealt with an iron fist. And we must make sure that it doesn't happen again."
Australia are strong favourites to take a 2-1 series lead, as India were 98-2 at stumps on the penultimate day after being set 407 to win.
India have already retained the Border-Gavaskar Trophy after winning the first two Tests, but following defeat in the third, need a win to be sure of a place in June's ICC Test Championship final against Australia at Lord's.
A draw or a defeat would leave the door open for Sri Lanka to take their place with a 2-0 series win over New Zealand. Sri Lanka need nine wickets to win the first Test on Monday's final day.
Defeat for India is very unlikely after Kohli scored his first hundred in the longest format since November 2019, his stunning 186 and Axar Patel's 79 lifting the hosts to 571 all out, with Australia reaching the close 3-0 to start their second innings.
With one day's play remaining, a draw will be the expected outcome, but the match will now be remembered for Kohli masterfully ending his drought.
He resumed on 59 with India on 289-3 and was scarcely troubled as Australia laboured on a slow pitch, allowing Kohli to bring up Test century 28 with a clipped single through square, bringing only a reserved celebration from the former captain but a rapturous reception from the raucous Ahmedabad crowd.
Commentator and former India coach Ravi Shastri proclaimed "a 600-kilo gorilla is off his back" and Kohli certainly played with freedom thereafter, reaching 150 with successive boundaries as he smacked a glorious cover drive and then threaded another four through midwicket.
His support was not as obdurate as Kohli but provided ample help in moving the scoreboard, Srikar Bahrat hitting two fours and three sixes in his 44 and Axar letting loose with five fours and four maximums.
Kohli eventually holed out at deep midwicket to bring the India innings to a close. His drought over, India will hope they have done enough to give him the opportunity to produce a similar display in London with the championship on the line.
Kohli ends 1,205-day drought
Not since scoring 136 against Bangladesh at Eden Gardens nearly three and a half years ago had Kohli reached three figures.
That is a remarkable amount of time for a player of Kohli's quality, which shone through as he scored his 75th international century, reaching that figure in 552 innings. Fellow India great Sachin Tendulkar took 566 to achieve the same feat.
Gavaskar mark equalled
Kohli's hundred was his eighth against Australia in Test cricket, moving him level with Sunil Gavaskar for the second most by an India batter. Tendulkar (11) still holds the record for centuries versus Australia in red-ball cricket for India.
Wicketkeeper-batsman Rahul scored a rapid 80 and had three dismissals behind the stumps as India scored a 36-run victory, defending a total of 340-6 by bowling out Australia for 304.
Rahul moved from number three to five in the batting order, with captain Kohli nudging up to three, as India adjusted their line-up after a 10-wicket thumping in the opening game of the series.
Kohli said: "I think it's very important to figure out what is the best team you can put on the park and when someone's batting as well as KL was batting today, it's very difficult to leave someone like that out.
"Batting at number five and batting like that for the team, this is probably the best he's played at international level according to me. That knock showed maturity and class.
"We know exactly what we're doing in the changing room. On the outside there's a lot of panic that we don't really focus on."
Kohli made 78, sharing a 103-run partnership for the second wicket with Shikhar Dhawan, whose 96 helped anchor the innings.
"Back to three was good for the team so I'm happy from that point of view that it helped the team," Kohli said.
Paying tribute to Dhawan, Kohli added: "In ODI cricket, he's been one of our most consistent performers. When he plays well it's a good sign for the team. I'm very happy that he scored runs as well. It always augurs well when Rohit [Sharma] and Shikhar both score runs."
Australia's ODI skipper Aaron Finch accepted his side had allowed India to put too many runs on the board.
"Yes, probably, but they played very well," Finch said.
"The whole way through the innings, we were probably one wicket shy of where we really needed to be to contain them at the back end and on an outfield like this with a good wicket and world-class players it can be hard to stop no matter what attack you've got."
Steve Smith's 98 kept Australia in touch, and Marnus Labuschagne made 46 in his first ODI innings, but Australia folded in the closing overs.
Ahead of the series decider in Bengaluru, Finch sent a message to his team, saying: "You just have to make sure that when you get in, you capitalise and you go really big.
"That's probably the area where we were slightly off tonight with the bat, just one wicket too many down as the run rate kept going up."
Rahane was afforded two lives en route to an unbeaten 104 for India, who reached 277-5 and a lead of 82 before stumps was called prematurely due to rain on Sunday.
It was Rahane's 12th Test ton and eighth away from home, his latest hundred coming from 195 balls as the tourists took control of the second Test.
The 32-year-old is also just the second Indian batsman to score a century on his first match as captain in Australia, joining Kohli in achieving the feat.
And Kohli, who has flown back home on paternity leave, took to social media to hail his team-mate's impressive display at the MCG.
"Another great day for us," he posted on Twitter. "Proper test cricket at its best. Absolutely top knock from Jinks @ajinkyarahane88."
Rahane and Ravindra Jadeja (40 not out) put on an unbeaten stand of 104 runs for the sixth wicket to frustrate Australia, who dropped four catches on the second day.
Indian opener Shubman Gill believes the patient batting of Rahane and Jadeja could prove decisive in the Test.
"I think it was a really valuable knock [from Jadeja]. He went into bat when we were 170-something for five," Gill told ANI.
"It's very easy for us to loosen up and let opposition back in the game. So, the partnership between Ajinkya Rahane and Jadeja was really important for us.
"The way Rahane played was so patient. This knock was all about patience.
"When you are playing such a high-quality bowling attack sometimes you go in that shell and you are not able to score runs. It was a magnificent knock to watch"
The tourists recorded their lowest ever Test score of 36 after a remarkable collapse in the day-night showdown on Saturday led to an eight-wicket defeat.
After resuming on 9-1 on day three, India were obliterated by an Australia attack spearheaded by Josh Hazlewood (5-8) and Pat Cummins (4-21), the former recording the most economical five-for by an Australian player in 73 years.
None of India's batsman reached double figures – Kohli was dismissed by Cummins for four – as they were routed in just 15.2 overs having tallied six runs fewer than their previous worst return set against England in 1974.
"We had a lead of 62-odd when we arrived today and just collapsed completely," Kohli said at the post-match presentation. "As I said, it is very hard to find words to express how everyone is feeling in the change room.
"When you work hard for two days, you play some good cricket to get yourself in a good position, and then literally [in an] hour you put yourself in a position where it is impossible to win. It really hurts.
"We didn't have enough intent batting today. We should have probably moved the game forward a little bit from the word go because we knew it was moving day and to get 100-odd ahead with wickets in hand would have been a good position to be in. It is something that needs to be reflected and learned from and we need to put up better performances going forward.
"It was pretty evident in the way we went about things: just losing one wicket after another. [That] just created an atmosphere where you felt like runs were so difficult to come by now. And [the Australian] bowlers obviously got more confidence and got a boost from that as well. It was a combination of both lack of intent and consistent areas from their bowlers as well."
In a warning to Kohli's men, Australia skipper Tim Paine – named player of the match after hitting 73 off 99 deliveries on Friday – said the hosts have plenty of room for improvement with the bat over the remainder of the series.
Paine's knock helped to carry Australia to a first-innings score of 191 after early struggles had left them at 79-5, with world-number-one batsman Steve Smith skittled for the loss of one run.
"At five for 79, if we lose another couple of quick ones then India are a long way ahead," Paine said. "To hang in to give our bowlers a chance to have a little crack under lights last night, then to have Pat start the day like he did and Josh Hazlewood from his very first ball was just on. When you are as tall and quick as our boys and they get it right, it can be an absolute nightmare. Full credit to our bowling attack again.
"[I'm] absolutely rapt with how we bowled in this Test, but we've still got a lot of work to do with our batting. Our first innings was well below what we'd expect – so it's a good thing to have a good win and not play anywhere near our best. It fills our team with confidence.
"I said this morning that I thought both these attacks have the ability to take really quick wickets - I didn't think they'd be coming that quick. We were expecting a real dogfight right to the end – late day four and maybe day five – but it shows the talent we've got the ball when our boys execute. If there's anything in the wicket that's what can happen."
For Kohli, attention now turns to the second Test on Boxing Day in Melbourne.
"You want to be committed to the team's cause and you want the team to perform really well," he said. "A result in this game would have been really nice.
"But I'm pretty confident that the boys going forward will reflect on this and they'll come out with a stronger performance on Boxing Day and try to get a result our way so that the series gets more interesting."
An ODI between Australia and New Zealand was played behind closed doors in March due to the coronavirus pandemic.
It remains to be seen when fans will again be allowed in to watch sporting events, with Australia due to host India from October.
Kohli is renowned for his ability to feed off crowds and Lyon joked the batsman could instead turn to the seats, although he was full of praise for the 31-year-old.
"He's probably good enough to adapt to any scenario," the off-spinner told a video conference on Tuesday.
"I was actually talking to Mitch Starc the other day and we actually said if we are playing with no crowd it would be quite amazing to see Virat try and rev up the seats.
"It's going to be a little bit different, but I think Virat, he's a superstar, he'll be able to adapt to any climate that we're able to play in."
While there is plenty of uncertainty over the series, Lyon said he was excited about welcoming India, who retained the Border-Gavaskar Trophy in 2018-19.
"I'm just excited about the prospect of India coming out. I think India coming out here to Australia, it's up there with the biggest series alongside the Ashes," he said.
"Obviously they're an absolute powerhouse of the cricket world so to have those guys out here is going to be fantastic. Playing in front of crowds or in front of no crowds, it's out of our control.
"We've got to be supported by and follow the advice from all the amazing medical people around the world giving out all the advice so it's out of our control.
"I haven't really thought about playing in front of no crowds or massive crowds, it's just about the opportunity about playing against India again.
"Obviously they had the wood over us last time they come out here, but I feel like we're a much stronger Australian cricket side at the moment and I'm just unbelievably excited about the prospect of playing them here at home."
Not even in the squad for the start of the series, Kuhnemann bowled a five-for on a poor pitch as India's first innings in Indore amounted to just 109 in 33.2 overs.
Marnus Labuschagne (31) and Usman Khawaja (60) then steered Australia into a comfortable position with a 96-run stand, as India's flagrant use of the DRS caused issues for the hosts.
While Ravindra Jadeja bowled Labuschagne to end that pairing, the tourists remained strong to finish the day 156-4 and hold a 47-run lead.
Australia came out of the blocks flying to take five wickets in the first hour, and seven in the first session.
Kuhnemann (5-16) and Nathan Lyon (3-35) had three wickets each, while Todd Murphy (1-23) trapped Virat Kohli lbw (22) to leave India 84-7 at lunch, before the hosts finished all out for 109 in just over a session.
India's response with the ball started well, Jadeja (4-64) taking Travis Head (9) lbw with just 12 runs on the board, and then bowled Labuschagne off a no ball – a mistake that proved costly.
Poor decision-making on DRS also contributed to the hosts' downfall, losing two reviews and opting not to challenge the umpire's call for an lbw on Labuschagne, which replays showed would have been out.
Australia welcomed those errors, Khawaja hitting a half century before being caught by Shubman Gill to put the tourists well on their way to fighting back in the series.
Kuhnemann's fine day
In just his second Test, Kuhnemann oversaw the undoing of India to finish with figures of 5-16.
Australia's charge saw six wickets tumble in just 22 overs, the most India have lost in the first innings of a match in this format since the beginning of 2007.
Jadeja's record
On a disappointing day for India, there was at least some comfort with the performance of Jadeja, who took all four of Australia's wickets.
He became just the second Indian player – and 11th cricketer overall – to take 500 wickets and score over 5,000 runs in the international game.
