India were just two wickets away from a victory in the third Test after Australia finished day four on Saturday, requiring 141 more runs to win in Melbourne.
A victory would mean either side earning a 2-1 lead in the four-Test series.
Australia were set 399 to win but following a top-order collapse, pace bowler Pat Cummins finished unbeaten on 61 to help the hosts reach 258-8.
Earlier, Cummins had taken a career-best 6-27 when India declared their second innings on 106-8 before lunch.
India had begun the day on 54-5, a lead of 346, with Mayank Agarwal making his way to 42 but captain Virat Kohli declared immediately when wicketkeeper Rishabh Pant fell for 33.
Australia then lost both their openers inside 10 overs as Aaron Finch was caught by Kohli at second slip for three, and Marcus Harris was caught at short leg off Ravindra Jadeja for 13.
The highest successful fourth-innings run chase at the MCG came in 1928, when England made 332-7.
Third Test, Melbourne (day four)
India 443-7 dec & 106-8 dec: Agarwal 42, Cummins 6-27
Australia 151 & 258-8: Cummins 61*, S Marsh 44, Jadeja 3-82