Virat Kohli and Axar Patel's 162-run stand for the sixth wicket helped India take a 91-run lead at the end of their innings.
Resuming at 289 for 3 on Sunday, India lost its first wicket of the day when Todd Murphy dismissed Ravindra Jadeja for 28. It was followed by Nathan Lyon dismissing KS Bharat for 44 runs.
Virat Kohli then stood tall with a solid 186 but missed out on what would have been his 8th Test double hundred.
Nathan Lyon and Todd Murphy picked three wickets apiece in the innings.
Coming out to bat again, Australia ended the day on 3 runs as openers Travis Head and Matthew Kuhnemann look to give the Aussies a good start with Australia trailing by 88 runs.