India lost five wickets in a hurry in the form of skipper Rohit Sharma (12), Shubman Gill (21), Cheteshwar Pujara (1), Ravindra Jadeja (4) and Shreyas Iyer (0).
Matthew Kuhnemann picked three wickets and Nathan Lyon the other two for Australia.
Australia's stormy beginning in the Test comes as they need to win the remaining two matches to level the Border Gavaskar Trophy.
India are ahead of Australia 2-0 in the four-match series.