Australia had appeared well poised as play resumed in Delhi, having edged the first innings by a run and ended the previous day on 61-1.
But hopes of levelling the series swiftly vanished as Pat Cummins' side were all out for 113 by lunch.
A routine chase of 115 was completed before tea, although Jadeja was the obvious star of the show for India with figures of 7-42.
He had removed Usman Khawaja the previous day, but it was Ravichandran Ashwin (3-59) who set in motion a remarkable stretch by having Travis Head (43) caught behind and then trapping Steve Smith.
Smith's partnership of 20 with Marnus Labuschagne would prove Australia's most productive of the day as the number three batsman was the next to go when Jadeja kept the ball low to bowl him for 35.
Ashwin got Matt Renshaw lbw, then Jadeja had Peter Handscomb caught in the slips to signal a drinks break. From the very next ball, the rampant Jadeja bowled Cummins with another low delivery.
Repeated attempts by Australia to sweep played into Jadeja's hands, and he quickly wrapped up the innings with the dismissals of Alex Carey, Nathan Lyon and Matthew Kuhnemann.
The final eight wickets fell for just 28 runs, and India's batsmen quickly capitalised despite losing KL Rahul in the second over.
Rohit Sharma scored 31, matched by Cheteshwar Pujara in an unbeaten innings as the hosts reached 118-4 inside 27 overs for a 2-0 series lead.
Day of joy for Jadeja
Jadeja's previous best figures had seen him take 7 for 48 against England back in December 2016, but he managed to improve on that stunning performance.
Indeed, the bowler needed only 12.1 overs this time – versus 25 against England – and required little help from his team-mates, bowling five of the six batsmen he removed on Sunday.
Milestone for Kohli
India did not need any heroes with the bat, but Virat Kohli was still able to pass a milestone in scoring 20 before he was stumped by Carey.
That short 31-ball innings took him past 25,000 runs for India across Tests, ODIs and T20Is.
A contest that had been largely dominated by India was never in doubt on day five, with the hosts needing another 241 runs with just four wickets remaining, Bangladesh could only add a further 52 runs as India bowled them out for 324.
Chasing a huge target of 513 at Zahur Ahmed Chowdhury Stadium, few would have expected the Tigers to muster much of a charge towards it, and Mehidy Hasan Miraz was walking back to the pavilion for 13 after Mohammed Siraj delivered a length ball that he tried to drive, only to find Umesh Yadav at backward point.
Captain Shakib Al Hasan was trying to put on a show at least, adding four more sixes to the two he hit on day four, before he finally fell to Kuldeep Yadav, bowled after trying a sweep shot for 84.
Kuldeep also dismissed Ebadot Hossain (0) before things were wrapped up when Axar Patel bowled Taijul Islam (4).
After the win was sewn up, India captain KL Rahul praised his team, admitting they were made to work hard even if the win was never really in doubt.
"It was a hard-fought Test, and I'm really happy we won," he said. "The pitch did flatten out, it did worry us, but in the first few innings it was difficult to get runs."
Shakib credited the victors and admitted that his team had not done enough with the bat.
"It was a good wicket to bat on, but we didn't bat well [in the first innings]," he said. "There should be no excuse. Lots of credit to India, as they created pressure."
The second Test begins in Mirpur on Thursday.
Kuldeep dominates with the ball
A fully deserved man-of-the-match award for the 28-year-old spinner Kuldeep, with final match figures of 8-113. Bangladesh just could not deal with Kuldeep, who also hit 40 with the bat in the first innings.
Patel continues to shine
Axar Patel took 4-77 in the second innings, and has now claimed 44 wickets after just seven Tests, the most by an Indian in the men's game after that number of matches, overtaking Ravichandran Ashwin's total of 43 wickets.
After Monday's play was washed out at a sodden Southampton, New Zealand finally moved on from 101-2 to post 249 in their first innings, captain Kane Williamson pointing the way with 49.
There were also useful runs from the lower order – Kyle Jamieson and Tim Southee contributed 21 and 30 respectively – as the Black Caps managed to overhaul India's total of 217.
Trailing by 32 as they came out to bat for a second time, India lost opener Shubman Gill, trapped lbw by Southee for eight, before they had erased the deficit in the final session.
Rohit Sharma also fell to the same bowler for 30 in the closing stages of proceedings, leaving Cheteshwar Pujara and Virat Kohli to see their side to the close. They will resume on 12 and eight respectively.
New Zealand will hope to make early inroads on the sixth and final day, which was added by the International Cricket Council as a provision for time being lost to bad weather.
Mohammed Shami helped restrict New Zealand's advantage with 4-76, including dismissing BJ Watling and Colin de Grandhomme as the Kiwis slipped to 162-6.
Yet the resolute Williamson remained, producing a crucial 177-ball knock that included six fours. His vigil finally came to an end when he was well caught by opposite number Kohli at a wide third slip off Ishant Sharma when one shy of a half-century.
Spin duo Ravichandran Ashwin and Ravindra Jadeja wrapped up the innings, though New Zealand's wagging tail means they appear the more likely winners on Wednesday.
Go-slow approach sees Kane able to move up
During his battling knock, Williamson surpassed Stephen Fleming (7,172) to become New Zealand's second highest run-scorer in Test cricket on 7,178, only behind current team-mate Ross Taylor (7,517) on the list. The latter reached a personal milestone while making 11, bringing up 18,000 international runs across all formats.
Shami shines with leather but still comes up short
Despite Kohli giving him every opportunity, Shami was unable to register his sixth five-wicket haul in Tests. The pace bowler produced a beauty to dismiss Watling, bowling the wicketkeeper for just one as India sensed the opportunity to seize a first-innings lead.
The hosts won by six wickets at Ekana Stadium but only just managed to reach the low target set by New Zealand during what seemed a poor innings that saw them finish on 99-8.
It was the first time the Black Caps had failed to reach 100 runs in a T20I against India, though it was not as bad as it first seemed on a difficult pitch.
Finn Allen's (11) reverse sweep attempt from Yuzvendra Chahal's (1-4) delivery saw him knock the ball on to himself and then the stumps for India's breakthrough, and Devon Conway (11) soon followed when caught behind by Ishan Kishan off Washington Sundar (1-17).
Glenn Phillips (5) was the third to fall victim to a botched reverse sweep, and Daryl Mitchell (8) also failed to reach double digits, with that pair removed either side of Mark Chapman (14) being run out.
Michael Bracewell (14) and Mitchell Santner (19 not out) formed one of only two stands to yield 20 runs, before New Zealand's innings petered out with only five in the final over.
India's response was not emphatic – they also failed to register a single six.
Shubman Gill (11) gave Allen an easy catch with a top edge off Bracewell (1-13) for an early boost, before Kishan (19) was run out and Rahul Tripathi (13) was caught at deep midwicket.
Suryakumar Yadav (26 not out) – aided ably by captain Hardik Pandya (15 not out) – ultimately dragged India over the line, getting just enough power on the penultimate ball to reach the boundary and take India to 101-4.
Suryakumar decisive when it counts
Having managed at least 47 runs in each of his previous three T20Is, Suryakumar is not used to struggling to amass significant totals.
Much like everyone else on Sunday, he could not quite find momentum with his 26 coming off 31 balls, but the fact he had the nous to be the only batter to break the 20-runs barrier should not be overlooked.
New Zealand bowlers give them a fighting chance
The batsmen should not take too much blame – pretty much all of them from both sides struggled on a wicket that Hardik criticised afterwards – but the Black Caps bowlers had plenty of work to do here.
The wickets did not tumble with quite the same regularity as when they were in bat, but with the ball they ensured the match remained tight – the fact they took it to the final over is commendable in itself.
Sharma, who declared his retirement from T20I's following India's success at the World Cup earlier this year, watched on as the Men in Blue started off a new era under the guidance of Suryakumar Yadav.
India comfortably beat Sri Lanka 3-0 in that series, and now face the same opponents in three 50-over matches that start this Friday.
Sharma will captain India for the upcoming fixtures, and acknowledged the difficulty in selecting the team's wicketkeeper batter for ODIs, with both KL Rahul and Rishabh Pant both in the mix.
Pant last featured in an ODI for India in November 2022, but has since made a comeback to the national team and was part of their T20 World Cup success in June.
First-choice Pant also played in two of the three T20s against Sri Lanka last month but faces competition from Rahul, who has been solid behind the stumps and impressed during the 2023 50-overs World Cup at home.
"It's a tough call. Both are quality players, you know the abilities of both. It's not easy to pick a team when you have players like that," Sharma told reporters.
"That's what these two individuals are all about. They're match-winners in their own way.
"It's always nice to have (such) problems. When you discuss a lot about whom to pick, it means there's quality in the squad. I look forward to these problems."
While Sharma has retired from the 20-over format, he is expected to stay in the role in 50-overs cricket with the Champions Trophy scheduled for next year.
The upcoming fixtures will present another difficult test for new head coach Gautam Gambhir, who is yet to taste defeat in his first three games in charge.
"We'll keep in mind what we want to achieve as a team but this is by no means preparation or practice (for the Champions Trophy). We want to play good cricket and get something out of the series. It's as simple as that," Sharma said.
"We don't want to think about trying this or that. Of course we want to try everything possible, but when you're representing the nation the quality of the cricket should remain the way it is and how we've played in the last few years.
"That's more important, more than thinking that it's a preparation so let's go out and chill in Colombo."
Sri Lanka, meanwhile, will be without pacers Matheesha Pathirana and Dilshan Madushanka, while Dushmantha Chameera and Nuwan Thushara are also out with illness and a fractured thumb.
Uncapped Mohamed Shiraz has been brought in as replacement as they look to bounceback from their whitewash defeat in their recent T20 series.
Smith scored his 27th Test ton as Australia posted 338 in their first innings at the SCG on Friday.
After resuming at 166-2, the hosts looked in position to put together a score of over 400, but aside from Smith (131) and Marnus Labuschagne (91), to go with Will Pucovski's debut half-century, their batting line-up largely struggled.
Ravindra Jadeja (4-62) did most of the damage for India, although they were unable to contain Smith.
The 31-year-old, who scored just 10 runs in the opening two Tests, looked back to his best, his latest Test century moving him level with Allan Border for the sixth most for Australia.
His eighth century against India also equalled the record for the most against the nation.
Shubman Gill (50) led India's response as they reached 96-2 at stumps, trailing by 242 runs, with Ajinkya Rahane (5) – who survived a late lbw review off Nathan Lyon (0-35) – and Cheteshwar Pujara (9) unbeaten heading into day three.
Josh Hazlewood (1-23) took a sharp return chance on his 30th birthday to remove Rohit Sharma (26) and Cameron Green took a good catch off Pat Cummins (1-19) as Gill departed, but India – coming off a win in Melbourne that levelled the series at 1-1 – looked otherwise comfortable.
Australia had appeared similarly at ease, but they lost 132-8 to finish their innings.
While Smith and Labuschagne's 100-run partnership was broken by a good catch by Rahane, Matthew Wade (13) played a loose shot before Jasprit Bumrah (2-66) made the most of the second new ball to remove Green (0) and Tim Paine (1).
Some late hitting from Mitchell Starc (24) boosted Australia as Smith accelerated before a brilliant piece of fielding by Jadeja ended the innings.
The tourists were four overs short of their target after time allowances were taken into consideration during the Black Caps' second-highest successful run chase in the 50-over format.
India captain Virat Kohli pleaded guilty to a sanction imposed by match referee Chris Broad, so a formal hearing was not required in Hamilton.
Ross Taylor made a magnificent unbeaten 109 not out and stand-in captain Tom Latham smashed a rapid 69 as the Black Caps ended a run of eight consecutive defeats with a four-wicket victory in their first game of the three-match series.
Shreyas Iyer (103) earlier struck a maiden international century and KL Rahul blasted an unbeaten 88 from 64 balls in India's 347-4, but New Zealand reached their target with 11 balls to spare.
Kohli said: "It was an outstanding performance by New Zealand, they batted outstandingly well. We thought 347 was good enough, but Ross is an experienced batsman and Tom's innings was the one that took away the momentum.
"Credit to Taylor and Tom. The opposition played better than us and they deserved to win. I think the debutants [Prithvi Shaw and Mayank Agarwal] gave us a good start and hopefully they continue.
"Iyer was outstanding getting his first ODI hundred under pressure, KL again. These are positives for us."
Australia looked in position to take a 2-1 series lead, needing eight wickets on the final day at the SCG, but were left frustrated by a stubborn India batting line-up and costly dropped catches.
Rishabh Pant (97), Cheteshwar Pujara (77), Hanuma Vihari (23 off 161 balls) and Ravichandran Ashwin (39 off 128 balls) helped ensure India were level heading into the final Test in Brisbane starting on Friday.
The SCG pitch played few tricks on day five, and Pant even had India dreaming of an amazing win, the tourists eventually finishing at 334-5, 73 runs adrift of a victory they stopped chasing after Vihari hurt his hamstring.
Josh Hazlewood (2-39) and Nathan Lyon (2-114) made breakthroughs, but Australia were unable to do enough in a Test they looked destined to win as Tim Paine dropped three catches.
Australia landed an early blow as Lyon had Ajinkya Rahane (4) caught at short leg by Matthew Wade.
But Pant – who suffered an elbow injury on Saturday – was put down twice by Paine, on three and 56, off Lyon, and he counter-attacked superbly to put the pressure on the off-spinner.
Pujara brought up 6,000 Test runs, the 11th Indian to achieve the feat as he continued to frustrate Australia.
Pant looked capable of leading India to a shock victory before falling just short of a third Test century, caught by Pat Cummins at gully after trying to attack Lyon again.
The second new ball brought a key wicket for Australia as Hazlewood produced a wonderful delivery to bowl Pujara.
A pair of reviews were unable to get Ashwin, who was dropped on 15, a diving Sean Abbott – on for the injured Will Pucovski (shoulder) – unable to hold onto a tough chance.
Vihari and Ashwin, showing no intent to score, remained stoic and defended well against an increasingly desperate Australia.
Paine dropped another chance after Vihari edged a Mitchell Starc (0-66) delivery and it proved to be the final opportunity as India held on for a draw.
Kohli, 33, announced his resignation as India Test captain on Saturday following a 2-1 series defeat to South Africa.
He had already called time on his reign as Twenty20 captain after the World Cup in the United Arab Emirates in late 2021, with Rohit Sharma taking that role before also replacing his team-mate as ODI skipper.
Kohli was left disappointed by a lack of communication by the Board of Control for Cricket in India (BCCI) before he was told he would be stood down as ODI captain, though Ganguly explained matters differently.
The BCCI president, by contrast, suggested he did not want Kohli to relinquish the T20 captaincy, while he stated India wanting only one white-ball captain as the reason for Kohli's removal as ODI skipper.
Nevertheless, Ganguly – who scored over 11,000 runs for India in ODIs – was quick to pay tribute to Kohli following his resignation.
"Under Virat's leadership Indian cricket has made rapid strides in all formats of the game," Ganguly wrote on Twitter.
"His decision is a personal one and BCCI respects it immensely. He will be an important member to take this team to newer heights in the future. A great player, well done."
Kohli led India a record 68 times in the longest format after initially captaining the Test side for the first time in 2014 against Australia before landing the role permanently the following year after MS Dhoni's retirement.
Only Graeme Smith, Allan Border, Stephen Fleming, Ricky Ponting and Clive Lloyd captained their country more often in Test matches.
Kohli is India's most successful Test captain with 40 victories and averaged a mammoth 54.80 during his tenure, scoring 20 centuries and making 18 half-centuries as he managed 5,864 runs from 113 innings.
KL Rahul was recently named vice-captain so is among the favourites to take the captaincy next.
Head coach Dravid has mild symptoms and is being supervised by the Board of Control for Cricket in India (BCCI) medical team.
The legendary former India batter will be able to join up with the team once he has tested negative.
India face fierce rivals Pakistan in their first match of the Asia Cup at the Dubai International Stadium on Sunday.
They will also take on a qualifier in Group A in a tournament that will be played with a Twenty20 format.
VVS Laxman stepped in to take over as head coach for the ODI series whitewash of Zimbabwe as Dravid was given a rest.
The Board of Control for Cricket in India (BCCI) issued a statement ahead of play on the fourth day of the game confirming Shastri will remain in the team hotel after undergoing further tests following the initial lateral flow result.
Bowling coach Bharat Arun, fielding coach R Sridhar and physio Nitin Patel are also isolating as a precautionary measure, having been identified as close contacts.
"They have undergone RT-PCR testing and shall remain in the team hotel and not travel with team India until confirmation from the medical team," a BCCI statement read.
"The remaining members of the team India contingent underwent two lateral flow tests – one last night and another this morning. The members upon returning negative COVID reports were allowed to proceed for day four of the ongoing fourth Test at The Oval."
India resumed on Sunday on 270-3 in their second innings, Rohit Sharma’s first Test century overseas helping them establish a 171-run lead over their hosts.
The series is level at 1-1 after England won by an innings at Headingley last time out. The fifth and final Test begins at Old Trafford in Manchester on Friday.
India's bowlers flexed their muscles after Australia's top order struggled to limp to 133-6 at stumps on day three – a lead of just two runs on Monday.
Australia lost 28-4 in 27.1 overs following tea to be left reeling in Melbourne, where India head into the fourth day needing just four tail-end wickets to win the second Test and level the four-match series.
Joe Burns' woes continued atop the order as Australia's batting fragility was exposed – Matthew Wade (40) and Marnus Labuschagne (28) the pick of the batsmen on a forgettable day.
India returned to the middle 277-5 and leading by 82 runs after capitalising on Australia's poor fielding display on Sunday.
Ajinkya Rahane's memorable innings came to an end on 112 – run out by Tim Paine after Ravindra Jadeja chased a half-century.
Rahane's 112 is the second-highest score by an India captain against Australia at the MCG, after Sachin Tendulkar's 116 in 1999, per Opta. Meanwhile, it is the fifth-highest by any visiting skipper overall.
Jadeja brought up his fifty before he was dismissed by star Australia paceman Mitchell Starc (3-78) and the hosts quickly cleaned up India for 326 as Nathan Lyon (3-72) and Josh Hazlewood (1-47) sent Umesh Yadav (nine), Ravichandran Ashwin (14) and Jasprit Bumrah (0) packing.
India had eyed a lead beyond 200 but instead claimed a 131-run advantage after surrendering 32-5 in 93 deliveries as their tail failed to wag.
In response, Australia crumbled early, especially Burns (four) – who could have been run out twice and faced an lbw appeal before he was caught behind off Yadav (1-5) in the space of just 10 balls amid growing scrutiny.
Yadav limped off injured and just as Wade and Labuschagne navigated Australia through 14 overs and to 38, Ashwin (1-46) drew an edge from the latter, which brought Smith to the crease and the former skipper was bowled around his legs by Bumrah (1-34) for eight.
Wade dug deep in a 137-ball display but his dismissal by Jadeja (2-25) opened the floodgates as Australia went from 98-3 to 99-6 when Travis Head (17) and Paine (one) – controversially out on review – were sent pack to the pavilion.
Cameron Green (17 not out) and Pat Cummins (15 not out) thwarted India but the pair and Australia face an uphill battle entering the penultimate day.
No play was possible on day two due to rain, but the Proteas made up for lost time by bowling the tourists out for 327 in a dramatic morning session.
The brilliant Lungi Ngidi took 6-71 as India lost seven wickets for 49 runs, KL Rahul falling for 123 and Ajinkya Rahane 48 after they had resumed on 272 in Centurion.
Kagiso Rabada provided great support for his fellow paceman, claiming 3-72, but India quickly shifted the momentum when South Africa started their reply.
Shami was outstanding, helping himself to 5-44 as the Proteas were bowled out for 197 in 62.3 overs, Temba Bavuma top scoring with 52, Quinton de Kock making 34 and Rabada 25.
Jasprit Bumrah (2-16) spent a long spell of the field with a sprained right ankle, but was able to return and end the South Africa innings, while Shardul Thakur chipped in with 2-51.
India closed on 16-1, leading by 146 runs, after Mayank Agarwal edged debutant Marco Jansen behind but Virat Kohli's side are well poised to take a 1-0 lead following a day that saw a record number of wickets fall in a Test at this venue.
Ngidi and Rabada tear through tourists
Rabada started the India collapse when he had Rahul caught behind in the fourth over of the day and De Kock took another catch to give Ngidi his fourth wicket, sending Rahane on his way three overs later.
Ngidi had his third five-wicket Test haul as Rishabh Pant could only fend a hostile short ball to Rassie van der Dussen short leg, with Rabada seeing the back of Ravichandran Ashwin and Thakur.
India were all out in a flash when Bumrah became Jansen's first Test victim after the excellent Ngidi drew an edge from Shami and De Kock snaffled a fourth catch.
Landmark for Shami as Proteas fold
Bumrah struck in the first over of the Proteas' reply, captain Dean Elgar edging behind, before Shami took centre stage.
Keegan Petersen chopped on to the third ball after lunch from Shami, who then produced a peach of a delivery to clean up Aiden Markram.
Shami's impeccable line and length, combined with a touch of movement of the seam, accounted for Bavuma caught behind just after he reached his half-century. Pant took another two catches for the 31-year-old, who became only the fifth Indian paceman to take 200 Test scalps.
Axar Patel struck three times to leave hosts Bangladesh on 272-6 at the end of day four of the first Test.
Chasing a huge target of 513 at Zahur Ahmed Chowdhury Stadium after tons from India's Shubman Gill and Cheteshwar Pujara, Bangladesh reached the end of day three with 42 runs on the board for no loss.
That stubborn resilience continued on Saturday as they made it to 124-0, before Najmul Hossain Shanto (67) was finally removed by Umesh Yadav early in the second session.
Yasir Ali was swiftly dismissed after facing just 12 deliveries, Axar picking up the first of his three wickets.
Zakir watched another of his partners fall when Litton Das (19) sent a Kuldeep Yadav googly into the waiting hands of Umesh at long-on.
The 24-year-old reached his debut hundred with a smart sweep for four, but an inside edge to Virat Kohli from Ravichandran Ashwin's full ball saw Zakir's stand come to an end.
Bangladesh's slim chances of victory were further dashed by a brilliant over from Axar.
The left-arm spinner first took out Mushfiqur Rahim's off stump before luring Nurul Hasan out of his crease, allowing Rishabh Pant to smash off the bails.
Axar finished day four with figures of 3-50 off 27 overs, with Bangladesh needing 241 runs from the final day for an unlikely victory, with captain Shakib Al Hasan and Mehidy Hasan Miraz at the crease.
Axar the pick of the bunch
Axar was the only India bowler to take more than one wicket, including those two in a superb 88th over of the innings.
He went for just 1.85 runs an over and is sure to play an important role on day five.
Zakir stars for hosts on debut
In his maiden Test for Bangladesh, Zakir was the man who kept the very slim possibility of a win for the hosts alive.
Bangladesh frustrated India in the first session, with Zakir's steady hands guiding them to 119-0 by the end of the first session.
While his team's innings eventually started to crumble around him, Zakir dug in to reach a memorable 100, which included 14 boundaries (13 fours, one six).
Dev, one of the great all-rounders, was taken to Fortis Escorts Heart Institute in New Delhi in the early hours of Friday morning after complaining of chest pain.
The 61-year-old, who captained India when they won the World Cup in1983, underwent an angioplasty and is expected to be discharged over the weekend.
A widely reported statement released by the hospital said: "Former Indian Cricket captain Kapil Dev, age 61 years, came to Fortis Escorts Heart Institute (Okhla Road) emergency department at 1:00 am on October 23 with a complaint of chest pain.
"He was evaluated and an emergency coronary Angioplasty was performed by Dr Atul Mathur, Director of Cardiology Department, in the middle of the night. Currently, he is admitted in ICU and under close supervision of Dr Atul Mathur and his team.
"Kapil Dev is stable now and he is expected to get discharged in a couple of days."
Support flooded in for Dev on social media, with the BCCI tweeting "Wishing the @therealkapildev a swift recovery. The nation is well aware of his grit and spirit and we are very sure he will be out of the hospital soon."
India captain Virat Kohli posted: "Praying for your speedy recovery. Get well soon paaji. @therealkapildev."
The legendary India batsman Sachin Tendulkar tweeted: "Take care @therealkapildev! Praying for your quick recovery. Get well soon Paaji."
Ravi Shastri, the India head coach and Dev's former team-mate, wrote: "Stay strong big brother. God bless."
After their capitulation in Adelaide, India responded in style at the MCG, chasing down a target of 70 relatively comfortably on day four.
Cameron Green (45) and Pat Cummins (22) helped Australia reach 200 as Mohammed Siraj took 3-37 for India.
But that set India just 70 for victory, and Shubman Gill (35 not out) and stand-in captain Ajinkya Rahane (unbeaten 27) ensured the tourists levelled the four-Test series at 1-1.
Resuming at 133-6, Green and Cummins managed to frustrate India until the second new ball.
But short balls from Jasprit Bumrah (2-54) and Siraj removed Cummins and Green respectively.
Siraj finished with five wickets on his Test debut. Syed Abid Ali (seven in 1967) is the only Indian man to have taken more having made their career debut in Australia.
Mitchell Starc (14 not out), Nathan Lyon (3) and Josh Hazlewood (10) provided limited resistance.
Bowled out for their lowest ever Test score of 36 in the second innings in Adelaide, there were some signs of nerves for India early in their chase.
Starc (1-20) had Mayank Agarwal (5) caught behind and Cheteshwar Pujara (3) was caught by Green off Cummins (1-22), but Gill and Rahane made sure of the victory.
The third Test is due to start in Sydney on January 7, although there remains uncertainty over where that will be held due to a coronavirus outbreak in New South Wales.
The tourists had embarrassed India in the first match, cruising to a 10-wicket win with unbeaten centuries from David Warner and Aaron Finch.
India posted a more challenging total of 340-6 on Friday, featuring 96 from Shikhar Dhawan, 80 from KL Rahul and Virat Kohli's 78, to give Australia a tricky chase and they fell short on 304 all out to set up a series decider in Bengaluru on Sunday.
At 220-3 with more than 12 overs remaining, Australia were firmly in the hunt, but India's bowlers got on top and the tourists did not recover from losing Steve Smith, whose 98 was the fulcrum of their innings.
Smith played on to give Kuldeep Yadav his second victim in the 38th over after dismissing Alex Carey to bring up 100 ODI career wickets.
Warner had earlier been dismissed for just 15, flicking at a length ball from Mohammed Shami (3-77) outside off stump and caught spectacularly above his head by Manish Pandey at cover.
Finch fell for 33 and Marnus Labuschagne made 46 in his first ODI knock, but Australia's hopes of a late flurry were savaged by Shami yorking Ashton Turner and Pat Cummins with the first two deliveries of the 44th over before Navdeep Saini and Jasprit Bumrah mopped up the tail.
Dhawan and Rohit Sharma had earlier put on a run-a-ball 81 for India's first wicket, before the latter fell for 42, pegged lbw by leg-spinner Adam Zampa.
Dhawan and Kohli kept the runs flowing, with their stand of 103 eventually broken when Dhawan, four short of an 18th ODI century and looking to reach three figures with one blow, was caught at fine leg by Mitchell Starc off Kane Richardson.
India had collapsed from 134 for one to 255 all out in Mumbai, but this time it would be a different story.
The classy Kohli scored at just over a run a ball before becoming the second of three victims for Zampa (3-50), before Rahul injected late pace into the scoring by plundering his 80 from 52 balls, clearing the ropes three times before being run out in the final over.
A blow for India on an otherwise positive day came with Dhawan taking a blow to the ribs when batting that prevented him from fielding.
Chasing down Australia's 90-5, India reached their target with four balls to spare after Karthik cracked the first delivery he faced for six and followed up with a pull for four.
The outfield was considered too wet for the T20I match to begin on time after rain earlier in the week, and ground staff worked to make it playable, even if only for a reduced-overs contest. Play eventually began after 21:30 local time.
Australia won the first match in Mohali on Tuesday, making this second contest in the three-game series a must-win fixture for the hosts.
After being put in, Australia captain Aaron Finch rattled to 31 at the top of the order, before Jasprit Bumrah took his leg stump, and wicketkeeper-batter Matthew Wade cracked a brutal 43 not out from 20 balls.
KL Rahul (10) and Virat Kohli (11) just about made it to double figures as India set about their chase, but it was captain Sharma who pinned the innings together, with four sixes and four fours in his 20-ball 46no.
Daniel Sams was trusted with the ball for the final over as Australia looked for some heroics, but the paceman was flogged over the ropes by Karthik from the first ball before sealing victory with another boundary. The series decider takes place in Hyderabad on Sunday.
Finch sees Australia fall short
Captain Finch ended his three-match run of sub-30 scores in T20Is, but his efforts were not enough to catapult Australia towards a sufficiently high score.
The skipper said at the post-match presentation: "We just got out-executed a little bit towards the back end there. Rohit played a great innings."
He said India bowler Axar Patel (2-13), who claimed the wickets of Glenn Maxwell and Tim David, had bowled two "brilliant" overs, that were "probably the difference in the game".
Rohit hails returning Bumrah
Jasprit Bumrah made a timely appearance in India colours, with the T20 World Cup in sight. Sidelined recently by a back injury, the star fast bowler satisfied captain Rohit as he took 1-23 from two overs.
"Coming back after a couple of months from a back injury can be tricky. We've got to give more time to him. it was good to see him on the park. That was important for us, and he got a crucial wicket," Rohit said.
"Slowly and steadily, he's coming back to his rhythm. It was good to see him bowling full throttle, but as a team we're not going to analyse this too much, we just want to let him come and enjoy his game."
Crawley hurried along to 31 from 33 balls but was first man down when he nicked Ravichandran Ashwin to first slip in the 10th over of England’s second innings.
The tourists took lunch on 89 for one, still 101 behind, with Ben Duckett settling well on 38no.
They started the day by taking the last three Indian wickets for 15 runs as they finished 436 all out in the morning session, Joe Root dismissing Ravindra Jadeja and Jasprit Bumrah with successive deliveries to collect four for 79.
Rehan Ahmed closed the innings when he spun one low through Axar Patel, ushering the game along to a crucial phase as England returned to the crease.
Having been bowled out for 246 inside 65 overs on day one, they knew they would need to do considerably more on a wearing pitch to have a chance of an unlikely success.
Crawley and Duckett made a typically positive start, clearing 45 from the deficit in the face of considerable scoreboard pressure. After two polite overs from Bumrah, it was spin at both ends and the initial signs were good.
Crawley sent a couple of reverse sweeps to the boundary boards before trying something even more expansive, moving his feet to the pitch and lifting Patel for six down the ground. It was a bold beginning but it ended all too quickly, Ashwin clipping the outside edge with a precise delivery that nestled in Rohit Sharma’s hands.
Ollie Pope started sketchily, busy but uncertain in his movements, but Duckett was poised. Trusting his arsenal of sweeps he hit five boundaries as he smothered the turning ball with some style.
Patel, 27, will sit out the first of four Tests after complaining of pain in his left knee following Thursday's training session.
As a result, spinners Shahbaz Nadeem and Rahul Chahar have been added to the squad, with the opening Test due to get underway in Chennai on Friday.
India are coming off a series victory over Australia, where they were depleted due to injuries in the blockbuster showdown.
Virat Kohli's India have managed to win each of their last 10 multi-game bilateral Test series played on home soil, that run beginning after they suffered a 2-1 series defeat at the hands of England in 2012.
No visiting men's Test side have beaten India at M.A. Chidambaram Stadium during the 21st Century (D3 L5) – Pakistan being the last team to do so in the format (1999).
England have managed to record five overseas Test wins in succession ahead of this match - their longest such run since 1914 (seven in a row between 1911 and 1914).
Joe Root is set to become the 15th man to appear in 100 Test matches for England and has the chance to equal Michael Vaughan's record of 26 Test wins as England skipper (currently 25).
