India were 120 for the loss of one wicket at stumps on the third day with Cheteshwar Pujara (10*) and Murali Vijay (42*) present at the crease.
Playing his 50th Test, opener Murali Vijay looked rock solid to remain unbeaten on 42.
The hosts lost just one wicket in KL Rahul who slammed another fine fifty before getting dismissed for 67 by comeback man Pat Cummins. Rahul and Vijay put up a 91-run-stand before the Karnataka right-hander got dismissed.
Earlier in the day, Ravindra Jadeja grabbed another five-wicket haul as hosts restricted Australia to 451 in their first innings. Indian bowlers made a great comeback on the second day as they picked up remaining six Aussie wickets by conceding just 152 runs.
Fast bowler Umesh Yadav also bowled well for figures of 3/106 while star off-spinner Ravichandran Ashwin bagged a wicket.
Resuming their batting from overnight score of 299/4, Australia couldn't do much damage as they kept losing wickets at regular intervals despite getting decent partnerships.
Australia skipper and their most dependable batsman Steve Smith remained unbeaten at 178 as wickets kept tumbling from the other end.
Smith stitched 50-plus partnerships with Matthew Wade and Steve O'Keefe but hosts came back strongly to restrict them.
Earlier at the day, Australia suffered a major setback in Glenn Maxwell (104), who brought up his career's maiden Test hundred, after his 191-run partnership with Smith was broken by Jadeja.
He hit 17 boundaries during the 361 balls he faced.
Glenn Maxwell, who returned to the Australian Test side after a lengthy period, scored his maiden century in the longest format of the game and put on a 191-run stand with Smith to help the visitors to a strong position after losing early wickets on the opening day.
The visitors started the day on a positive note with Maxwell bringing up the first runs of the day with a boundary.
The right-hander quickly completed his maiden century in the longest format of the game, reaching the landmark by guiding an Umesh Yadav delivery to the third man boundary.
Jadeja completes another fifer:
For India, left-arm spinner, Jadeja, was the pick of the bowlers. He completed another five-wicket haul by grabbing four wickets on the second day and was almost unplayable. He finished with 5/124 after bowling a whopping 49.3 overs in the first innings.
Maxwewll, who is playing in only the fourth Test of his career, departed shortly afterwards when a Jadeja delivery landed on the off-stump line and spun away viciously. The ball kissed the outer edge of Maxwell's bat and Indian wicketkeeper Wriddhiman Saha pulled off an excellent catch.
Maxwell scored 104 runs off 185 balls with nine hits to the fence and two sixes. It was a rare display of patience and endurance from the right-hander who had scored only 80 runs in the three Tests he had played previously in his career.
Matthew Wade joined Smith in the middle and the duo proceeded to add 64 runs between them before Jadeja struck twice in quick succession.
Wade seemed to be in good form, scoring 37 runs off the 50 balls he faced. He seemed on track for a half-century but was outfoxed by a Jadeja delivery which kept straight after pitching.
Wade, who played for the turn, only ended up handing an edge to Saha.
Pat Cummins survived all of two deliveries before Jadaja bowled him with a beautiful delivery. The ball landed on the middle and leg stump line and spun away viciously, beating the outside edge of the bat to hit the off-stump.
Jadeja almost dismissed Smith in the last over before lunch, but the ball landed just short of the slip cordon.
Steven O'Keefe was the first to fall after the lunch break as he mistimed an attempted pull of a Umesh delivery which was pitched just short of good length. The ball hit the top edge and lobbed up for Vijay at fine leg.
Nathan Lyon fell in the next over with Karun Nair pulling off an excellent reflex catch off Jadeja's bowling.
Jadeja then came up with an excellent bit of fielding to help run out Josh Hazlewood thus bringing Australia's first innings to an end.
(With inputs from agencies)