India reduced Australia to 227/8 at tea on day four, still needing 307 runs to win.
Travis Head and Mitchell Marsh scored 89 and 47 respectively.
Wicketkeeper-batter Alex Carey is unbeaten at 30 from 39 balls.
Jasprit Bumrah and Mohammed Siraj have picked three wickets each.
India on Sunday ended their second innings at a mammoth score of 487/6 declared, riding on young Yashasvi Jaiswal's 161 and veteran Virat Kohli's unbeaten 100 which saw the batter's strong comeback after a dull period.