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.
CAF to investigate post-match violence at Africa Cup of Nations
Violent confrontations at the conclusion of two of the Africa Cup of Nations quarter-finals at the weekend are to be investigated with possible sanctions to be imposed, the Confederation of African Football (CAF) said.
At 37, Kohli reinvents himself to extend ODI dominance
Virat Kohli has tweaked his approach to counter-attack early in his innings and put bowlers under pressure to flip the momentum for India, the batting stalwart said after his match-winning knock in Sunday's one-day international against New Zealand.
Barcelona edge Real Madrid in heated Spanish Super Cup final
Raphinha has scored twice as Barcelona won the Spanish Super Cup after an intense 3-2 victory over Real Madrid in Sunday’s final in Jeddah.
India beat New Zealand in first ODI as Kohli misses out on ton
India has beaten New Zealand by four wickets in the first one-day international in Vadodara on Sunday where the in-form Virat Kohli fell agonisingly short of his 54th ODI hundred.
Former world number three Raonic hangs up his racket
Canada's former world number three Milos Raonic has announced his retirement from tennis at the age of 35 on Sunday after winning eight ATP tour titles and more than $20 million in prize money over a decade and a half on the circuit.
