India posted 571 in reply to Australia's first-innings total of 480 to claim a 91-run lead in the fourth and final Test on Sunday.
Virat Kohli top-scored for the home side with a mammoth 186 while opener Shubman Gill (128) also smashed a hundred.
Spinners Nathan Lyon and Todd Murphy claimed three wickets apiece for Australia.
For India, who lead the series 2-1, Shreyas Iyer could not bat because of back pain.
Man City down Al-Ain 6-0 to reach Club World Cup knockout stage
Ilkay Gundogan scored two goals as Manchester City comfortably dispatched Emirati club Al-Ain 6-0 on Sunday to ease into the knockout stage of the Club World Cup from Group G along with Juventus.
India 96-2 in second innings after Brook leads England comeback
India finished day three on 90-2 to lead England by 96 runs at stumps in the opening test at Headingley on Sunday after England were dismissed for 465 in the first innings on the back of Ollie Pope's century and Harry Brook's knock of 99.
Alcaraz beats Lehecka in Queen's final to send Wimbledon statement
Top seed Carlos Alcaraz edged powerful Czech Jiri Lehecka 7-5 6-7(5) 6-2 to claim his second Queen's Club title and send out a powerful statement ahead of his Wimbledon defence on Sunday.
Dubai Basketball Club set for historic EuroLeague debut
Dubai Basketball Club has been selected to compete in the prestigious EuroLeague for the first time, after the organisers announced its expansion from 18 to 20 teams in late May.
England steady the ship with Brook after India remove centurion Pope
India dismissed England's overnight centurion Ollie Pope early on the third day of their opening test at Headingley on Sunday but Harry Brook helped the hosts to reach 327-5 in their first innings and they trailed by 144 runs at lunch.
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