At break, Cheteshwar Pujara was unbeaten after a gritty innings during which he posted a patient 46 off 141 deliveries, with Ravichandran Ashwin was batting on 5 at the other end.
The visitors have only themselves to blame for their troubles as most of their top order batsmen virtually threw away their wickets by going after deliveries which they should have left alone.
After a poor first session which saw the fall of four wickets, Pujara and Rohit Sharma tried to stem the rot with a partnership of 45 runs.
However, spinner Nathan Lyon took two wickets during the post lunch session to plunge the Indians into deeper trouble.
Rohit, who scored 37 runs off 61 balls, seemed to be in good touch and set for a big score.
But attempted big shot off Lyon's bowling handed an easy catch to Marcus Harris.
Despite the regular fall of wickets at the other end, Pujara continued to bat patiently, carefully avoiding the big shots and playing the ball along the ground.
But Lyon delivered another blow shortly before tea when Rishabh Pant edged one to the slip cordon.
Earlier, a disciplined bowling attack by Australia left India at 56/4 at lunch.
Opting to bat, the visitors were off to a disastrous start as opener K.L. Rahul's (2) thick edge was superbly taken by Aaron Finch at third slip off a Josh Hazlewood delivery with just three runs on board.
Soon, Murali Vijay (11) also followed his partner after falling in the seventh over, leaving India at 15/2.
With the addition of just four runs in the visitor's scorecard, pacer Pat Cummins gave a huge blow to India after packing back skipper Virat Kohli (3), thanks to a stunning catch by Usman Khawaja at gully.
Pujara and Rahane (13) then tried to put things back in control, adding 22 runs for the fourth wicket however, Hazlewood struck again in the the 21st over to dismiss the latter.
Incoming batsman Rohit Sharma and Pujara then played some sensible cricket as India crept past the 50-run mark.
India: 143/6 (Cheteshwar Pujara 46 batting, Rohit Sharma 37; Josh Hazlewood 2/28, Nathan Lyon 2/51) vs Australia at Tea on Day 1.