Australia are 6-133 with Cameron Green (17no) and Pat Cummins (15no) at the crease, after India were eventually bowled out for 326.
Stand-in captain Ajinkya Rahane finished up 112 while Ravindra Jadeja made 57, with their 121-run sixth wicket partnership laying the foundation for the tourists.
India were unable to add many runs early on day three, eventually bowled out for 326, losing their last five wickets for 32 runs.
Joe Burns failed again at the top of the order for Australia, while Matthew Wade (40) and Marnus Labuschagne (28) both got starts.
Steve Smith didn’t last long again as his lean series continued, dismissed bowled by Jasprit Bumrah.
Travis Head only made 17, before Tim Paine got a tough DRS call to be dismissed for 1.
Rahane’s century as stand-in captain was full of application and grit and he was delighted with his 11th Test century.
“It feels really special, especially when captaining the side,” Rahane said.
“Getting a hundred is always special, but my best knock, I feel, is still at Lord’s when I got 103 (in 2014).”
An India victory would level the series at 1-1 after they lost the First Test in Adelaide when bowled out for 36 and having since lost Virat Kohli.
“We’ve still got four wickets to go, the game is not over yet,” Rahane said.
“We have to come stronger tomorrow, bowl in the right areas and get the victory.”