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 thump Chelsea to move closer to Arsenal
Manchester City reignited the Premier League title race on Sunday, scoring three goals in 17 second-half minutes to crush Chelsea at Stamford Bridge and move within six points of leaders Arsenal.
Sinner beats Alcaraz in Monte Carlo final to top rankings
Italy's Jannik Sinner dethroned defending champion Carlos Alcaraz 7-6(5) 6-3 in Sunday's Monte Carlo final to claim his first Masters title on clay and snatch back the world number one ranking from the Spaniard.
Tottenham stay in bottom three after defeat by Sunderland
Tottenham Hotspur's relegation fears deepened as manager Roberto de Zerbi's first game in charge ended in a 1-0 defeat by Sunderland that left the London club third from bottom of the Premier League on Sunday.
Andreeva fights back to beat Potapova in Linz Open final
Top seed Mirra Andreeva overcame a first-set wobble to clinch her second title of the year, beating local favourite Anastasia Potapova 1-6 6-4 6-3 to win the Linz Open on Sunday.
Coach Golemac leaves Dubai Basketball
Dubai Basketball and head coach Jurica Golemac mutually agreed to part ways with immediate effect on Sunday.
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