Fellow opener Rob Yates also cracked 191 in an extraordinary first-wicket partnership of 343 with outstanding skipper Davies, whose unbeaten 226 came from 274 balls with 25 fours and three sixes.
To compound the misery for promoted Durham, who had won the toss, Will Rhodes reached 60 not out to take the hosts past maximum batting points and to 490 for one before the close.
Champions Surrey took command against Somerset at The Oval despite a century from Tom Lammonby.
Lammonby (100) and Matt Renshaw (87) got Somerset off to a fine start by putting on 178 for the second wicket but the loss of seven wickets for 20 runs undermined their efforts.
Captain Lewis Gregory (50) lifted the score to 285 but Cameron Steel (four for 50) wrapped up the innings before Surrey openers Rory Burns and Dom Sibley chiselled 42 off the lead without loss.
Joe Clarke continued his excellent start to the season with another century as Nottinghamshire closed on 305 for six against Worcestershire at Trent Bridge.
Following up his ton against Essex last week, Clarke hit 105 and shared in a third-wicket stand of 133 with Ben Slater (70) as the hosts recovered from the loss of two early wickets.
Dean Elgar (120) scored his first Essex century and Matt Critchley (103no) also reached three figures against Kent at Chelmsford.
Jordan Cox added 67 and Michael Pepper 49 as the hosts amassed 421 for six at stumps.
Hampshire were 305 for six at the end of day one against Lancashire at the Utilita Bowl.
Liam Dawson was unbeaten on 61 after solid efforts from Tom Prest (85), James Vince (56) and Nick Gubbins (50).
Australia’s Nathan Lyon (two for 97) bowled 32 overs as Lancashire kept themselves in the game.
In Division Two, spinner Alex Thomson took a career-best seven for 65 as Derbyshire bowled out Glamorgan for 287 in Cardiff. Kiran Carlson was the hosts’ top-scorer with 74.
Derbyshire were 46 for one in response.
Emilio Gay’s unbeaten 165 helped Northamptonshire to 311 for three against Middlesex at Wantage Road. Captain Luke Procter added 73 in a second-wicket partnership of 189.
Pakistan captain Shan Masood’s 140 was the mainstay of Yorkshire’s 326 against Gloucestershire at Bristol. Jonathan Tattersall (58) and Matt Milnes (51) also contributed but Zaman Akhter’s five for 89 helped the hosts hit back before they ended the day on 28 for two.
Liam Trevaskis was 82 not out as Leicestershire closed on 326 for eight against Sussex at Grace Road. Rishi Patel (87) and Peter Handscomb (51) also hit half-centuries.
Australia headed into day five requiring just six wickets to take a 2-0 series lead, Joe Root's side batting only for a draw, given they needed an improbable 386 runs for victory.
Any chance of England escaping without defeat hinged on the shoulders of Ben Stokes and Jos Buttler, after the tourists' captain Joe Root fell to Mitchell Starc (2-43) on the final ball of day four.
Australia flew out of the blocks, Starc removing Ollie Pope – caught at slip by stand-in captain Steve Smith – and Nathan Lyon picking up the crucial wicket of Stokes, who was dismissed for a 77-ball 12.
Buttler and Chris Woakes then lived charmed lives, with the wicketkeeper edging Starc between a motionless Alex Carey and David Warner, while the right-arm all-rounder survived a caught-behind review from Lyon having not scored.
That England partnership lasted 31 overs before Woakes was bowled by Richardson, with Ollie Robinson following soon after as he was caught at slip by Smith off Lyon.
Stuart Broad successfully reviewed a leg before wicket decision to make it into the final session, but Buttler (26) fell in bizarre fashion, stepping on his own stumps after a 207-ball stint at the crease.
Richardson fittingly removed James Anderson, caught in the gully by Cameron Green, as England made it 12 Tests without a win in Australia (D1, L11); their joint-longest run without a victory Down Under (also 12 matches between January 1937 to February 1951).
England head to Melbourne for the Boxing Day Test needing a win to stand a chance of regaining the Ashes, while a draw would ensure Australia retain the urn yet again.
Buttler battles to no avail
Buttler, who before the Ashes insisted he would play with a carefree with "nothing to lose", battled against Australia almost single-handedly on Monday, but even his best efforts were not enough against a relentless Australia.
It was a mixed bag of a Test for the 31-year-old, who took some stunning catches, but also dropped some golden chances behind the stumps.
Contrasting fortunes under the lights
England's rear-guard almost masked multiple selection issues across the Gabba and the Adelaide Oval, but what cannot be denied is Australia's magnificent pink-ball form.
The hosts have won all nine of their day-night Test matches, the most by any side and the only team with a 100 per cent record, while England have lost each of their last four games in the format – last winning against West Indies in August 2017. Richardson was the pick of the bunch for the hosts, sealing his five-for when he dismissed Anderson.
The news comes on the morning of the first day of the pink-ball Test at Adelaide Oval, with Queensland fast bowler Michael Neser confirmed to replace Cummins in the XI for his debut on Thursday.
Former skipper Steve Smith will captain Australia in the absence of Cummins in the day-night Test in Adelaide.
Cummins was dining at a restaurant on Tuesday and was sat nearby to someone who has since been confirmed as a positive coronavirus case.
The star paceman did not breach any biosecurity protocols and isolated as soon as he became aware of the situation. Cummins has since had a PCR test, which produced a negative result.
However, Cummins has been confirmed as a close contact by South Australia Health and will be required to isolate for seven days, ruling him out of the second showdown with rivals England.
Cricket Australia (CA) said it anticipated Cummins will be available to play in the Boxing Day Test at the MCG in Melbourne.
"Cummins is understandably very disappointed not to be able to captain Australia for the day-night Test in Adelaide," CA said in a statement.
The 28-year-old fast bowler had led Australia to a nine-wicket victory in the Ashes opener as skipper in Brisbane, after taking over from Tim Paine.
Smith's deputising marks the first time he will have captained his country since the controversial 2018 sandpaper-gate Test match in Cape Town, which led to his dismissal as skipper and 12-month suspension.
Australia may have dodged a further bullet, revealing Mitchell Starc and Nathan Lyon were also dining at the same restaurant but at a separate table outdoors.
Both have been deemed casual contacts by SA Health and are free to play.
Australia celebrated a comprehensive victory at the Gabba, where England lost eight wickets in the morning session to set the hosts just 20 runs to win, which they scored post-lunch with the loss one wicket.
Lyon had become only the third Australian bowler to reach 400 wickets as England capitulated all out for 297 in Brisbane on Saturday – the spinner leading his nation's charge with 4-91.
England emerged on the fourth day with renewed hope after Joe Root and Dawid Malan mounted a fine rear-guard on Friday – the pair's stance leading the tourists to 220-2.
But England's revival quickly diminished as they crumbled and were eventually all out before lunch – losing eight wickets for just 77 runs.
Lyon sparked the collapse in the fourth over of the day, the milestone man got Malan (82) to edge onto his pad for Marnus Labuschagne to take a sharp catch at silly mid-off with the second new ball approaching, snapping a 162-run partnership.
Root added three runs to his overnight score before he fell to Cameron Green (2-23) and Ollie Pope (4) followed his captain back to the pavilion the very next over after attempting to cut a Lyon delivery, instead punching to Steve Smith at slip.
Australia sniffed blood and England simply had no answer as Pat Cummins (2-51) and Josh Hazlewood (1-32) got the wickets of Ben Stokes (14) and Jos Buttler (23), with Lyon cleaning up the tail, alongside Green.
After lunch, Marcus Harris (9 not out) hit the winning boundary to clinch Australia's victory following Alex Carey's dismissal for 9.
Lyon joins exclusive club
Before Lyon, only Shane Warne (708) and Glenn McGrath (563) had taken 400 wickets or more for Australia. The spinner joined the club after finally ending his quest for the milestone, having waited almost a year. Lyon became the seventh spin bowler to take 400 wickets in men's Test cricket.
Carey makes history
The Gabba opener marked a Test debut for wicketkeeper Carey, who stepped in behind the stumps after former skipper Tim Paine opted to take a break from cricket. Carey capitalised, marking his bow with eight catches – becoming the first player in Test cricket to achieve the number on debut.
Root's 24 on Sunday may have seen him overtake Alastair Cook (4,844) to become England's top run-scorer as Test captain, but the current skipper had little to celebrate barring yet another personal landmark in a fantastic 2021 for the Yorkshireman.
The tourists started positively, dismissing nightwatchman Michael Neser (3), Marcus Harris (23) and Steve Smith (6) in quickfire fashion to leave the hosts 55-4.
However, Marnus Labuschagne (51) and Head (51) fought back, before Cameron Green (33 not out) and Mitchell Starc (19) guided Australia to their declaration total of 230-9, setting England a mammoth 468 to win.
Rory Burns (34) and Dawid Malan (20) offered some brief resistance after Haseeb Hameed had been removed for a duck by Jhye Richardson, but the pair were soon sent packing to leave Root and Ben Stokes (3 not out) to try and save the day.
Root, though, fell to Starc's final delivery after he had earlier been hit in the groin by the left-arm quick, and Head appreciated what a big wicket the England captain was.
"Root is a huge wicket, he is in fantastic form," Head told reporters after play ended on the penultimate day at the Adelaide Oval with England 82-4.
"I have a lot of sympathy for him – it wasn't a great time to get hit.
"We got told to give him some space [on the pitch]. Starc on that line is never pretty and unfortunately with the day he [Root] has had it wasn't a great time to get hit.
"They've still got some quality players. Nathan Lyon will play a massive part, the ball is turning. It's a big day tomorrow."
England will need what would seemingly be a miracle on Monday, with Stokes – who delivered unlikely heroics at Headingley in 2019 against the same opposition – leading the charge.
England's fast-bowling coach Jon Lewis expressed his support for Stokes, who he believes is the best man for the task ahead, while hailing the valiant efforts of Root.
"Anytime one of your best players [Root] gets out, it's a knock," Lewis told reporters.
"Joe showed a hell of a lot of character to go out. There was no doubt in Joe's mind he was going out to bat and it shows what a great player and brilliant leader he is.
"Since he got hit he stood up, he could have had a nightwatchman. He wants to show his team how hard he wants to try for the team.
"They will try to survive the day tomorrow to get ourselves out of this game with a draw. It's a big ask I know."
"Ben [Stokes] has done it before, he has done special things in an England shirt."
Lyon became only the third Australian to achieve the feat in Saturday's nine-wicket victory over rivals England inside four days at the Gabba.
After almost a year of waiting, Lyon brought up the milestone as Australia claimed 77-8 to roll England for 297 in the first session in Brisbane, where the tourists had resumed on 220-2 before the sensational collapse.
Australia were set 20 runs for victory and easily reached the total following lunch, despite the loss of Alex Carey, but it was all about Lyon after the first Test.
"Relief, because I'm not so much on personal milestones I had a lot of banter going on so it probably wasn't on my mind a lot more," Lyon told reporters after finishing 4-91 to take his Test haul to 403 from 101 matches.
"But I say the next wicket is hardest to get but yes, it was a big relief."
Before Lyon, only Shane Warne (708) and Glenn McGrath (563) had taken 400 wickets or more for Australia.
Lyon – who had waited since January to join the exclusive club – also became the seventh spin bowler to take 400 wickets in men's Test cricket.
"It hasn't really hit me to be honest," Lyon, 34, said. "I'll get my phone and call my family and friends and that will probably hit a little closer to home.
"But it's something I'm very proud of, there's no doubt about that. It's been some hard toil to get it, but very rewarding."
Asked if he was less nervous now after ending his wait, Lyon replied: "I'm nervous because I care. I care about everyone in that changing room, I care about the result and playing cricket and representing Australia. I'm not nervous because I'm scared of failing.
"[Captain] Pat [Cummins] was extremely calm as captain... I think when Australia play their best cricket, we're calm and playing with smiles on our faces and enjoying it. Pat really hit that home."
Australia leads the series 3-0 after three dominant victories ahead of the fourth Ashes Test starting on Wednesday at the SCG.
There has been speculation about the make-up of the Australian side given they have already secured a series victory with dilemmas on Josh Hazlewood's fitness and Scott Boland's place along with talk of a second spinner in Mitch Swepson.
Lyon, who has taken 12 wickets in the three Tests, insisted Australia were determined to pursue victory and pick the best side possible.
"There's no more dead rubbers - and I've never considered them when you wear a baggy green - firstly because there's the World Test Championship and we want to go 5-0 up," Lyon told reporters on Sunday.
"If the conditions suit then we pick the best team to win that Test to make sure we keep moving forward. The Ashes for me is the pinnacle but I'd love to be part of a Test Championship final to state our case for the number one team in the world."
Australia missed out on the World Test Championship final last year, finishing third behind winners New Zealand and India. The Aussies have won the past two Ashes on home soil 4-0 and 5-0 respectively.
Lyon endorsed fellow spinner Swepson, who is set to get Test opportunities in 2022 with tours of Pakistan, Sri Lanka and India to come.
"I love bowling in partnership with spinners for sure," Lyon said. "I've done it a lot in subcontinent conditions so if the opportunity does come to play two spinners I know we'll really enjoy building that partnership. We've been doing it in the nets but it's a lot different."
Hazlewood, who has missed the past two Tests with a side injury, is expected to train fully with the group on Monday and could replace Boland who took 7-6 in the second innings of the third Test.
Australia captain Cummins was force to sit out the match at Adelaide Oval after the paceman was deemed to be a close contact with a positive coronavirus case at a restaurant.
Fellow fast bowler Starc and spinner Lyon dined at the same establishment, but were considered to be casual contacts with the person who had the virus.
Starc took 4-37 and Lyon claimed 3-58 as England meekly collapsed from 150-2 to 236 on day three in reply to 473-9 declared. Australia then closed in complete command on 45-1 in their second innings - leading by 282 runs.
Left-arm quick Starc revealed it could have been a very different story if Cummins had replied to his text message.
He said: "It was just fortunate we were sitting outside. It was almost a bit of a p***-take because Pat didn't reply to my message so thought we'd sit away from him and sit outside so it's been a lucky one."
Starc says he did not lose any sleep fretting over whether dining out could have cost him another chance to exploit England's vulnerable batting line-up in a match Josh Hazlewood was ruled out of due to a side strain.
"Spinner [Lyon] didn't sleep. I slept quite fine, there wasn't much I could do about it after," he said.
It was revealed on Saturday that both sides will face stricter protocols for the Melbourne and Sydney Tests due to a rise in COVID-19 cases.
Players can only follow Starc and Lyon's lead and dine outside, while they must also socially distance with members of the public.
Cricket Australia chief executive Nick Hockley told SEN radio: "We need to make sure there's social distancing, so we ask everyone to be respectful in the public.
"That's the real shame because what we have seen is players wanting to interact with fans. That's been a feature of the Big Bash. But we've now got very clear protocols.
"As it comes to those on the field of play we need to make sure that people are operating in a really biosecure way."
The West Indies collapsed to lose 35-6, with the defeat confirmed within an hour-and-a-half of the resumption of play, as Michael Neser claimed three of the six fourth day wickets in his second Test match.
The tourists had resumed at 38-4, chasing an improbable target of 497, but were all out for 77.
Left-arm Mitchell Starc grabbed the opening two wickets of the fourth day, including an inswinging gem to clean bowl Jason Holder.
Nathan Lyon took his 450th career Test wicket, when he bowled a heaving Alzarri Joseph who had danced down the pitch. Lyon was denied another when Travis Head dropped a chance close in from Marquino Mindley.
Neser, who finished with 3-22, closed out the job with wicketkeeper Alex Carey pulling off an excellent one-handed catch off his bowling to dismiss Mindley for a duck.
Carey took four catches on Sunday, including a brilliant juggling pluck when he stood up at the wicket off Neser's bowling to remove Joshua Da Silva who offered the only real resistance from the tourists on the fourth day with 15 from 40 balls.
Local batsman Head was named Player of the Match after scoring 175 from 219 deliveries in Australia's first innings, which set up the win. Marnus Labuschagne was named Player of the Series after making 502 runs in two Tests, the most-ever by an Australian in a two-match Test series.
Day-night dominance
Australia's win means they have claimed 11 from 11 victories in day-night Tests, relishing the pink ball conditions. Australia are also seven from seven in Adelaide in recent times.
The 419-run victory was also Australia's largest-ever win by runs against the West Indies, who had not lost a Test this calendar year prior to this lopsided series.
Quick turnaround for Aussies
Australia will be delighted to have secured victory with more than a day to spare, given they are due to take on South Africa in a three-match Test series starting Saturday.
Josh Hazlewood is highly unlikely to be available for the first Test against the Proteas due to a side strain, with Neser and Scott Boland vying for that spot, assuming Pat Cummins is fit to return.
The Proteas had resumed 15-1 on the fourth day chasing the improbable target of 387 to make the hosts bat again, but were all out for 204 with the tea break delayed with play extended before the 10th wicket fell.
Spinner Nathan Lyon led the way with 3-58 while Mitchell Starc bravely bowled through pain with an injured finger, taking the opening wicket of the fourth day to finish with 1-62.
Temba Bavuma offered the Proteas' toughest resistance with 65 across more than three hours, but had little support, with Kyle Verreynne the next best with 33.
The tourists were not helped by two run outs on the fourth day, but they appeared a side deflated by the task at hand and the gulf in quality.
South Africa had got through to lunch at 120-4 with Bavuma and Verreynne combining for a 63-run stand, but when the latter was trapped LBW by Scott Boland, the side quickly fell apart in the second session.
Lyon trapped Marco Jansen LBW before Keshav Maharaj was run out by Marnus Labuschagne, with Australia's off-spinner dismissing Bavuma and Kagiso Rabada in quick succession shortly after, before Steve Smith bowled the wild-swinging Lungi Ngidi to seal victory.
Warner crowned for double hundred
Opening batsman David Warner was named Player of the Match after his second-day double century, which reinforced his worth in the side, having come into the game under pressure to hold his spot. Warner's century, coming in his 100th Test match, was the 25th of his Test career.
Walked wounded for Aussies
Australia's victory means they have an unassailable lead in the series but they have a list of headaches ahead of the third Test in Sydney next week. Mitchell Starc and Cameron Green both have finger injuries, with both set to miss the game at the SCG, while Lyon required treatment on day four for a shoulder concern. Australia's next Test series after this is in India in February.
The Proteas had resumed 15-1 on the fourth day chasing the improbable target of 387 to make the hosts bat again, but were all out for 204 with the tea break delayed with play extended before the 10th wicket fell.
Spinner Nathan Lyon led the way with 3-58 while Mitchell Starc bravely bowled through pain with an injured finger, taking the opening wicket of the fourth day to finish with 1-62.
Temba Bavuma offered the Proteas' toughest resistance with 65 across more than three hours, but had little support, with Kyle Verreynne the next best with 33.
The tourists were not helped by two run outs on the fourth day, but they appeared a side deflated by the task at hand and the gulf in quality.
South Africa had got through to lunch at 120-4 with Bavuma and Verreynne combining for a 63-run stand, but when the latter was trapped LBW by Scott Boland, the side quickly fell apart in the second session.
Lyon trapped Marco Jansen LBW before Keshav Maharaj was run out by Marnus Labuschagne, with Australia's off-spinner dismissing Bavuma and Kagiso Rabada in quick succession shortly after, before Steve Smith bowled the wild-swinging Lungi Ngidi to seal victory.
Warner crowned for double hundred
Opening batsman David Warner was named Player of the Match after his second-day double century, which reinforced his worth in the side, having come into the game under pressure to hold his spot. Warner's century, coming in his 100th Test match, was the 25th of his Test career.
Walked wounded for Aussies
Australia's victory means they have an unassailable lead in the series but they have a list of headaches ahead of the third Test in Sydney next week. Mitchell Starc and Cameron Green both have finger injuries, with both set to miss the game at the SCG, while Lyon required treatment on day four for a shoulder concern. Australia's next Test series after this is in India in February.
Pat Cummins (3-34) and Mitchell Starc (3-51) did most of the damage as Australia dismissed the tourists for 283, before finishing on 29-1 in their second innings to establish an overnight advantage of 344 runs.
Debutant Tagenarine Chanderpaul was at least able to reach his half-century before edging Josh Hazlewood to David Warner for 51, before Nkumrah Bonner retired hurt on 16 after taking a Cameron Green delivery to the head.
Australia struggled to get rid of West Indies captain Kraigg Brathwaite (64) until he was bowled by a terrific delivery from his opposite number Cummins to bring up his 200th Test wicket.
Starc dismissed Kyle Mayers (1) and Jermaine Blackwood (36) either side of Nathan Lyon getting rid of Jason Holder (27), before Starc had Joshua Da Silva out for a duck with a delivery that swung back spectacularly into the stumps.
Australia cleared up the tail with minimum fuss to leave the hosts heading into their second innings with a big advantage.
Warner began aggressively but almost paid the price as he was nearly run out on 13, though Usman Khawaja (6) was heading back to the pavilion soon after when a nothing shot at a Kemar Roach ball was edged through to Da Silva.
Warner (17 not out) and Marnus Labuschagne (3 not out) saw Australia through to the close and will be confident of building an even bigger lead on the penultimate day in Perth.
200 up for Cummins, Lyon also reaches landmark
It was a fitting way for Cummins to reach 200 wickets, emphatically dismissing his fellow skipper. In his 44th Test, he became the fifth-fastest Australian to 200 behind only Clarrie Grimmett (36), Dennis Lillee (38), Stuart MacGill (41) and Shane Warne (42).
Lyon also had reason to celebrate as his 2-61 took him past Dale Steyn on the all-time Test wicket-taker list, moving up to ninth place on 440, just two behind Ravichandran Ashwin.
West Indies allow faint hope to fade further
It is never easy replying to such a mammoth first innings score, with Australia posting 598-4 dec, but the tourists were ticking along nicely, reaching tea on day three on 237-4.
However, they collapsed once Starc started to wobble them, adding just 46 for their final six wickets.
Only 54.2 overs were bowled at the Gabba on Saturday as India reached 62-2 in response to Australia's first-innings 369.
Heavy rain delayed the start of the final session before a wet outfield meant play was abandoned.
Tim Paine scored a half-century for Australia as T Natarajan (3-78), Washington Sundar (3-89) and Shardul Thakur (3-94) took three wickets each for India.
Rohit Sharma (44) wasted his start as he tried to attack Nathan Lyon (1-10) after Pat Cummins (1-22) had Shubman Gill (7) caught at second slip by Steve Smith.
Cheteshwar Pujara (8) and Ajinkya Rahane (2) were unbeaten when stumps were called, with India 307 runs adrift in the final Test of a series that is locked at 1-1.
Injury-hit India continued to fight and they only need a draw to retain the Border-Gavaskar Trophy.
Australia, though, will also lament some of their batting that could have put India under more pressure.
Starts squandered as tail wags for Australia
Marnus Labuschagne made a century on Friday, but four other batsmen made more than 36 but failed to go on for Australia.
Paine (50) and Cameron Green (47) joined that group on day two as they squandered promising starts, with Lyon (24) – playing his 100th Test – and Mitchell Starc (20 not out) lifting Australia beyond 350.
Reckless Rohit hurts India
Like many in the Australia line-up, Rohit wasted another opportunity to put together a big score in Brisbane.
He looked in control before attempting to take on Lyon one too many times, and a running Starc took a good catch. The 33-year-old is one of India's more experienced players and his dismissal left the tourists at 60-2. It comes after he made scores of 26 and 52 in Sydney.
The 36-year-old trapped Faheem Ashraf leg before wicket after a review in Perth to reach his personal landmark on day four of the first Test as the hosts cruised to a 360-run victory.
Lyon, whose achievement was delayed by injury during last summer’s Ashes series, is the third Australian to reach the mark, following in the footsteps of the late Shane Warne and Glenn McGrath.
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Only Muttiah Muralitharan, who leads the way with a remarkable 800, Warne, James Anderson, Anil Kumble, Stuart Broad, McGrath and Courtney Walsh have claimed more Test scalps.
Lyon told Channel 7: “It’s something I’m very proud about. Firstly, to take 500, it’s a bloody big milestone. I still pinch myself when I see my name next to those guys – well not even next, below those guys in my eyes.
“Shane Warne is the greatest to ever play this game in my opinion, and Glenn McGrath’s record speaks volumes, doesn’t it? So to edge closer to those guys, it’s something that I’m proud of.”
Lyon’s big moment arrived at the start of the 28th over of Pakistan’s second innings when he rapped Faheem’s pads, but saw concerted appeals turned down by umpire Richard Illingworth.
However, the Australians opted to review and were belatedly given the verdict they craved by TV umpire Michael Gough with the ball shown to be hitting leg stump.
Faheem’s departure left Pakistan on 79 for seven and Lyon also accounted for Aamer Jamal as they slumped to 89 all out.
The right-armer, who made an instant impact on his Test debut against Sri Lanka in 2011 when he dismissed Kumar Sangakkara with his first ball, finished with match figures of five for 80.
Warner scored an unbeaten 111 to lead Australia to 217-2 declared in their second innings and a mammoth lead of 416 runs on day four at the SCG on Monday.
And New Zealand's horror tour in the trans-Tasman series finally came to an end after being dismissed for 136 during the final half-hour, as Matt Henry did not bat due to injury.
Ross Taylor (22) made history by becoming New Zealand's all-time leading Test runscorer, however, it was another forgettable day for the visitors as Australia spinner Lyon (5-50) finished the match with 10 wickets.
The Black Caps were reduced to 4-2 inside five overs after Mitchell Starc (3-25) tore through openers Tom Latham (1) and Tom Blundell (2), while Lyon and Pat Cummins (1-29) joined in to leave New Zealand reeling on 38-5 after tea.
Taylor was skittled by a stunning Cummins delivery in the over after surpassing Stephen Fleming for his country's record as Australia steamrolled New Zealand inside four days for the third consecutive Test.
Colin de Grandhomme (52), BJ Watling (19) and Todd Astle (17) provided some resistance but Australia showed their class to remain undefeated in their home season.
Tim Paine's side resumed on 40-0, with Warner and his under-pressure opening partner Joe Burns setting about building upon an already commanding lead of 243.
Only two wickets fell as Warner celebrated his third century of the Australian summer and 24th of his career – taking his tally to 786 runs at 131 against Pakistan and New Zealand.
Burns added 24 to his overnight score when he was trapped lbw by Astle (1-41), for 40 despite originally being given not out.
Marnus Labuschagne (59) contributed a quick-fire half-century – his seventh score above 50 in eight innings – before going out swinging to Matt Henry (1-54).
Australia's innings also featured a five-run penalty after umpire Aleem Dar ruled Labuschagne and Warner ran down the protected area of the pitch – the five runs added to New Zealand's first innings, improving it from 251 to 256.
In the final analysis, it made scant difference.
The tourists lost their first two red-ball games to the hosts, including a dramatic batting collapse in Delhi that cost them the chance of regaining the Border-Gavaskar Trophy.
But they recovered to seize victory in the third Test in Indore, thanks to Nathan Lyon's record-breaking spell with ball-in-hand - which saw him become the highest wicket-taker in Tests between Australia and India - during their nine-wicket triumph, one which saw them qualify for the World Test Championship final.
That bounce-back has impressed McDonald, especially after losing six wickets of their own for just 11 runs during the first innings, with the coach thrilled by their resolve.
"You have almost got to be near perfect against India in India," he said. "I think this game besides that 6 for 11 was near perfect.
"We had a little bit of luck [but] we took our opportunities as well. You compare that to the Delhi game. We had one hour of chaos there and that cost us that Test match when we'd played pretty good cricket."
"We came here and doubled down on what we'd set out to achieve at the start of the tour. So on the back of Delhi, it was 'how clear are we going to be in what we need to do next'".
On Lyon's second-innnings 8-64, McDonald added: "We go out there and Nathan Lyon as the experienced spinner delivers one of his best performances. It always takes an individual to do something special to get the team back on track, no doubt about that."
Australia will have the chance to tie the series when they meet India in their final red-ball game in Ahmedabad, starting on Thursday.
The spinner followed up his 84 from India's innings victory in the first match of the series, this time making 74 in a rearguard action as the hosts fought back from 139-7 to post 262 all out.
That meant Australia held a one-run first-innings lead, with Nathan Lyon taking 5-67, and the tourists reached 61-1 at the close batting for a second time at the Arun Jaitley Stadium in Delhi.
India began the day on 21-0 but soon began to unravel. KL Rahul (17), captain Rohit Sharma (32) and Cheteshwar Pujara (0) departed in the space of three overs, with India sliding from 46-0 to 54-3 as Lyon gobbled up each wicket, bowling Rohit and getting two lbw verdicts.
Shreyas Iyer (4) soon followed, and although Virat Kohli and Ravindra Jadeja added 59 for the fifth wicket, when the latter was dismissed lbw for 26 by Todd Murphy it heralded another collapse. Kohli became the fourth lbw victim of the innings when he fell to Matthew Kuhnemann for 44, and Srikar Bharat (6) did not hang about, leaving Axar and Ravichandran Ashwin with the task of salvaging something.
They proved up to the job, adding 114 for the fourth wicket before Ashwin (37) fell to Pat Cummins with the new ball, a loose delivery down the leg side flicked to Matt Renshaw at square leg. Axar was then caught brilliantly by Cummins off Murphy, ending hopes of a maiden Test century.
Australia, ultimately relieved to avoid a first-innings deficit in this latest instalment of the Border-Gavaskar Trophy series, then saw Travis Head's 39no help them overcome the early loss of Usman Khawaja (6) before the close.
David Warner will miss the rest of the game due to concussion, and has also suffered a hairline elbow fracture, it was announced earlier in the day.
Lyon closes in
Lyon took his Baggy Green career haul to 496 wickets, putting him on the brink of becoming the sixth Australia bowler to reach 500 at international level. A long-format specialist, some 466 of Lyon's scalps have come in Tests.
With the breakthrough wicket of Rahul, Lyon became the second Australia player to reach 100 wickets in all formats against India, after Brett Lee, who took 111 wickets. This haul also took him to 100 wickets in Border-Gavaskar Trophy matches.
Axar keeps hosts in touch
Axar's innings was a terrific concoction, as he struck three sixes and nine fours before going after another powerful shot and perishing to an exemplary catch from Cummins. He went wicket-less during 12 overs with the ball in Australia's first innings, but this was another reminder he is in the team as a bowling all-rounder.
He made a modest 249 runs in his first 13 Test innings, but has plundered 158 from his last two knocks.
Pakistan skipper Babar's century on Tuesday set up a thrilling conclusion at the National Stadium and the contest was in the balance right until the end.
Babar eventually fell four runs short of a double century, while Rizwan was unbeaten on 104 to help Pakistan survive a record 172 overs in the fourth innings.
The hosts are nine Tests unbeaten against Australia at this venue and, having also played out a draw in Rawalpindi, it is now all to play for in the third and final Test in Lahore.
Pakistan started day five on 192-2 in their second innings, leaving them needing 314 runs to pull off a record chase, and hopes were high when Babar resumed play.
Babar and Abdullah Shafique crossed 200 runs, marking just the fourth time a third-wicket double century partnership had been notched in the fourth innings of a Test.
Australia wrestled back some control when Pat Cummins removed Shafique for 96 just before lunch, with Steve Smith redeeming himself for an earlier drop.
Fawad Alam (nine) succumbed to Cummins, but Babar continued to add runs and looked set for a deserved double ton.
However, he was eventually dismissed for 196 by Nathan Lyon, who then removed Faheem Ashram for a duck to keep things finely poised.
Having fended off Australia for so long, Pakistan then lost Sajid Khan (nine) and were 414-7 with eight overs remaining.
Rizwan looked to be next to go, only for Usman Khawaja to spill the chance, and from there the right-handed batsman brought up his hundred in the penultimate over.
Unable to take the final three wickets, Australia were left to rue what might have been as Pakistan reached 443-7 – 63 runs short of victory – to claim a famous draw.
Babar inspires Pakistan fightback
Babar had gone over two years without a Test century prior to reaching three figures on Tuesday and went on to add another 94 runs on the final day in an inspiring display.
Flanked by supporting roles from Rizwan and Shafique, Babar, whose innings lasted 425 balls, batted for more than 10 hours in the end, though he would have loved to have reached a double century.
Lyon's best efforts not enough
All of Pakistan's hard work was nearly undone thanks to a late flurry of wickets for Lyon, who ended with figures of 4-112.
Removing Babar was a key moment in a match that proved gripping from the start, in stark contrast to a mundane first Test, and sets up a gripping finale next week.
Paine stepped down from his Test captaincy role last Friday over a historical investigation into lewd texts sent to a former Cricket Tasmania colleague in 2017.
The 36-year-old, who at the time was found not to have breached Cricket Australia's conduct code and remained captain, is still in Australia's Ashes squad to face England, though a new leader is yet to be announced.
Batter Marcus Harris previously stated Paine has "got all the support of the players" and Lyon has echoed that sentiment towards the wicketkeeper, who was appointed captain in 2018 following Steve Smith's ball-tampering scandal ban.
"I can 100 per cent guarantee he has the full support of the Australian changeroom," Lyon told reporters as Australia prepare for the first Ashes Test on December 8.
"I don't see him as a distraction at all. Come the Gabba Test match and throughout the whole series, we are professional sportspeople, and we will go out and do our job.
"Tim made a mistake, he's owned it, for me that shows great courage to be honest. Tim has got my full support. I am looking forward to catching up as soon as we get out of quarantine.
"In my eyes, Tim is the best gloveman in the country, in the world.
"The selectors said they were going to pick the best available XI and in my eyes Tim Paine is the best keeper in the world. I want him. This is very selfish, from a bowler's point of view, I want the best gloveman behind the stumps."
Off-spinner Lyon and wicketkeeper Paine have formed a strong partnership for Australia but failed to combine for a single wicket against India in the Test series loss last time out.
Since then, Paine has undergone neck surgery in September before returning to action for Tasmania's second XI against South Australia.
Pat Cummins and Steve Smith have reportedly been interviewed by Cricket Australia amid ongoing speculation the pair will step in as captain and vice-captain respectively, much to Lyon's excitement.
"You have a bowler's mindset and a batter's mindset rather than two batters; they can come together and really come up with some good guidance," Lyon said. "I am excited by the fact we are potentially going to have a bowler as captain."
Australia will head to the Gabba with added confidence as well after their T20 World Cup win in the United Arab Emirates, and Lyon claimed there is still a buzz around the camp despite Paine's resignation.
"The mood is incredible," he said. "On the back of the boys winning the World Cup, there are only nine guys here who were part of that, but the staff too, there is an unbelievable feeling in the Australian cricket changerooms right now.
"Our preparation is flying along. I'm ready to go."
Stand-in captain 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.
Australia were woeful in the field, dropping four catches at the MCG, where Mitchell Starc (2-61) was left visibly frustrated after Travis Head spilled a catch to dismiss centurion Rahane with what proved to be the final ball of the day.
India resumed on 36-1 – in response to Australia's 195 in the second Test – after dominating the opening day in front of a capped Melbourne crowd and the tourists only lost four wickets to take control.
Shubman Gill (45) and Cheteshwar Pujara (17) did not last long as India fell to 64-3 following a masterful spell of bowling from star Australia paceman Pat Cummins (2-71), before the patient and anchoring Rahane got to work in the middle.
Tim Paine put down Gill in the second over of the day off the bowling of Josh Hazlewood (0-44), but the Australia captain made amends when he combined brilliantly with Cummins for two wickets.
Hanuma Vihari added 21 runs before he was sent packing by spinner Nathan Lyon (1-52) – bringing Rishabh Pant to the crease.
Explosive wicketkeeper Pant produced an entertaining 29-run cameo off 40 deliveries, but it came to an end when Starc broke through for his second wicket of the innings.
It brought up a milestone for Starc, who celebrated his 250th Test wicket, as Paine recorded his 150th dismissal.
Supported by Ravindra Jadeja (40 not out), Rahane posted his 12th Test ton and eighth away from home following the tea break – a boundary bringing up a memorable hundred from 195 balls.
