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.
US keep Super 8 hopes alive with 31-run win over Namibia in T20 World Cup
The United States kept their hopes of reaching the Twenty20 World Cup's Super 8 stage alive as they ended their Group A campaign with two straight wins, after beating Namibia by 31 runs on Sunday.
Sweden's Ponsiluoma shows nerves of steel to win men's pursuit gold
Martin Ponsiluoma held his nerve and hit his final five shots to win the men's 12.5km pursuit Olympic race in spectacular fashion on Sunday to finally secure a biathlon medal for Sweden at the Winter Games.
Holder, Hope help West Indies thump Nepal, make T20 World Cup Super Eight
West Indies charged into the Super Eight Stage of the Twenty20 World Cup after the two-times champions defeated Nepal by nine wickets in Mumbai on Sunday, with Jason Holder's four-wicket haul and Shai Hope's half-century setting up the win.
Banton blitz lifts England past Scotland in T20 World Cup
England beat Scotland by five wickets in the Twenty20 World Cup on Saturday to move up to second in Group C thanks to Tom Banton's unbeaten half-century at Eden Gardens.
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