Earlier, Nathan Lyon kept Australia in the contest, claiming six for 82 to help bowl out Bangladesh for 221 after the hosts had resumed on 45 for one.
Former Australia captain Steve Smith said he is desperate to recover lost ground ahead of next year's World Cup by competing in the IPL after being left so deflated by the ball-tampering scandal that getting out of bed became a struggle.
Kohli's skill and spikiness on the field reminded many of their own: Australian media
Steve Smith believes India is one of the toughest places to play Test cricket and winning a five-day format series in the country is a major career goal for him. Smith also heaped praise on India's spin all-rounder Ravindra Jadeja, describing him as a difficult bowler to face in the subcontinent.
Australia pacer Josh Hazlewood claimed the Men's Test Player-of-the-Year award. It marked his first Australian Cricket Award, with Hazlewood taking 30 wickets at just 13.16 in Tests against the West Indies, New Zealand, and India.
Joe Root became England's most successful batter after he became the first batter from his nation to go past the 19,000-run mark
Hat-trick man Jasprit Bumrah attains highest rating points by an India seamer since since Kapil Dev in 1981.
Former Australia batsman Brad Hodge said current skipper Steve Smith will continue to accumulate runs in Test cricket and could surpass the likes of Sachin Tendulkar.
South Africa captain Faf du Plessis defended Quinton de Kock again on Thursday, suggesting Australia's opening batsman David Warner had crossed a line in his sledging of the wicketkeeper in the tempestuous first Test.
After condemning Steve Smith's conduct during the Cape Town Test on Sunday, Shane Warne struck a more supportive tone on Wednesday.
It was the wicket-keeper's second Test and it must have been pure joy to be there at that glorious moment when victory was achieved.
Australia will be without their premier pacers but their envious pedigree in ICC tournaments make them favourites to progress to the semi-finals of the Champions Trophy from Group B.
The Indian batters' inability to grind it out against a relentless Australian pace attack in testing conditions left the team precariously placed at 51/4 at the end of a rain-marred day three.
'A lot to work on but this is the blueprint of the way we want to play Test cricket and hopefully we'll keep doing that.'
Smith was stripped of the Australian captaincy on Sunday and suspended for one Test by the International Cricket Council after admitting a team plot to tamper with the ball in the on-going third Test against South Africa at Newlands.
IMAGES from the 3rd ODI between India and Australia played in Rajkot on Wednesday
Akash Deep and Jasprit Bumrah saved India the blushes in the Brisbane Test with a resolute 10th wicket partnership but the rookie pacer on Sunday said his focus was on a wholesome contribution to the team rather than looking to "merely save the follow-on".
Former India captains have called on cricket authorities to investigate Australia skipper Steve Smith amid allegations his team flouted the rules of the game when deciding whether to review decisions during the second Test.
'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.'
Opener David Warner and all-rounder Mitch Marsh will be rested for the five-match Twenty20 International series against Sri Lanka next month to prepare for the upcoming tour of Pakistan.
It was an engrossing day of cricket with both India and Australia trying to seize control in front of a big Sunday crowd at the M Chinaswamy Stadium in Bengaluru and a lot of words were exchanged in the first session between India's fielders and Australia's batsmen.
No matter where India is playing, the Men in Blue always have their loyal followers cheering them on.
A concussed Smith was ruled out of the third Test, starting at Headingley on Thursday, after being struck in the neck by a vicious bouncer from England paceman Jofra Archer.
IMAGES from Day 2 of the opening Ashes Test played between England and Australia at Edgbaston Cricket Ground in Birmingham on Saturday.
Australia's mouthwatering clash with India sees the two behemoths of the modern game go head-to-head in five tests over six weeks with the tourists eyeing a third straight series triumph Down Under.
Keeping a lid on emotion will be nearly as important as executing gameplans for both India and Australia when the world's top two teams continue their captivating series with the third Test in Ranchi on Thursday.
Soon after the BCCI banned the duo from the upcoming Indian Premier League, Smith and Warner were each hit with 12-month bans by the national body for their roles in ball-tampering scandal during the Cape Town Test against South Africa last month.
The debate over the vacant slot at the top of the Australia batting order continues to captivate the nation's sports media a month before the opening clash in a blockbuster five-Test series against India.
'I had a good two months in India with the Indian Premier League and we are really excited about this tournament'
Captain Steve Smith raised a composed century to push Australia to a 22-run first innings lead in the second Test against Pakistan but the home side's hopes of pushing their advantage were washed away by rain on day four on Thursday.
'The past few days I have found something ... I have found my hands which I am extremely excited about.'
Images from Day 1 of the fifth Test between Australia and India at the Sydney Cricket Ground on Friday.
Back-to-back Test series wins over Australia are almost unheard of but India have won the last four they have played.
Steve Smith and David Warner may wake with some relief on Thursday as they greet the final day of their ball-tampering bans
How the world reacted to Smith, Bancroft and Lehmann
'Not taking away any credit from India, but when they won in Australia, there is no doubt that Australian cricket was going through a turmoil and there were problems in their dressing room'.
Australia Captain Pat Cummins and fellow pacer Mitchell Starc show off their newest prized possession to the Australian media on Tuesday, November 28, 2023.
Nathan McSweeney had a disappointing start to his international career after being ousted by Bumrah for 10 and zero in the first Test at Perth.
Images from Day 1 of the first Test between Australia and Pakistan, in Brisbane, on Thursday.