Opener Matt Renshaw, who had retired due to upset stomach before lunch, was unbeaten on 38 at the break and giving him company was Mitchell Marsh (2).
Australia, who lost opener and vice captain David Warner in the pre-lunch session for 38, lost the wickets of captain Steven Smith (27), Shaun Marsh (16) and Peter Handscomb (22).
Spinners Ravichandran Ashwin (1/37) and Ravindra Jadeja (1/43) struck late blows to send back Smith and Handscomb respectively after Jayant Yadav outsmarted Shaun Marsh earlier in the second session.
The visitors, apprehensive about the behaviour of the dry track, were more enterprising in the first session when openers Warner and Renshaw were at the crease as they put on 82 in 27.2 overs.
But once they departed, the scoring rate dropped drastically. Skipper Smith cut out all frills and played a dour knock while Shaun was slightly more aggressive in making 16 before falling to Jayant.
Handscomb was caught right in front of the wicket by Jadeja with a quicker, straight ball and five balls later Ashwin had Smith caught at mid-wicket coming down the track in a rush of blood.
Handscomb batted for 45 balls while Smith faced 95 balls and struck just two fours.
India almost had next man Mitchell Marsh sent back caught behind off Ashwin in the same over in which he dismissed Smith, but a review of the decision revealed he had not nicked the turning ball.
Earlier, Warner was looking good before he was bowled for 38 by Umesh and then tall Renshaw retired to the pavilion with an upset stomach close to lunch, which resulted in the arrival of two new batsmen in captain Steven Smith and Shaun Marsh at the crease.
For India, the bulk of the bowling was done by their spin trump card Ashwin, who opened the attack with Ishant Sharma.
Ashwin bowled 16 overs for 23 runs without a wicket to his name.
Umesh, brought into the attack after 27 overs, bowled two overs for one run and ended up with the wicket of Warner, who played away from his body and dragged the ball on to his stumps.
Opting to take first strike in the first-ever Test held in this city, Australia initially did struggle a bit against the turning ball.
They managed to score 40 runs in the first hour of play with Warner starting slowly and then attacking off-spinner Jayant Yadav.
Warner was also lucky to be bowled off a no-ball by Jayant when on 16.
PTI