Young opener Yashasvi Jaiswal hit a brave half-century on Monday to keep Australia at bay as India reached 112-3 at tea, with high hopes of escaping the fourth Test with a draw.
The 23-year-old Jaiswal overcame a shaky start to hit 63 off 159 balls while Rishabh Pant was on 28.
The duo batted the second session of the final day in an unbroken 79-run partnership after India lost three wickets just before lunch.
With at least 38 runs still to be bowled, India need another 228 overs to reach their target of 340, while Australia need seven wickets to take a 2-1 lead in the final Test in Sydney, starting on Friday.
But the possibility of an equalizer began to loom as Jaiswal and Pant adopted a risk-free approach to the home attack, showing signs of running out of ideas as the ball began to age.
Unlike the period with the new ball before lunch, Australia struggled to create chances and Jaiswal looked more comfortable than when he was routinely beaten by fast bowlers Pat Cummins and Mitchell Starc in the first session.
Australia’s best hope could lie in taking the lead with the second new ball, although it will only become available with about an hour to play.
India showed no appetite in the face of what could be a record fourth-round chase in Melbourne to take a 2-1 lead in the five-match series.
The cheap dismissals of veterans Rohit Sharma, KL Rahul and Virat Kohli were a major setback as India slumped to 33-3 at lunch.
Kohli was out on the last ball before half-time, having scored just five when he attempted to cross from Starc and edged Usman Khawaja at the first over.
Australian captain Cummins hit a breakthrough double in the 17th over and took 2-19, continuing the impressive all-round performance in which he scored 49 and 41 with this bat.
Rival skipper Rohit had batted with discipline but fell when trying to use an aggressive whip across the line which flew quickly to Mitchell Marsh in the gully.
The off-form Rohit failed to pass 10 in three Tests after missing the opener in Perth upon the birth of his second child.
India were 25-1 at that point and it quickly became 25-2 when Rahul fell five balls later, sneaking a rising Cummins delivery to Khawaja at first slip.
Earlier, Australia’s stubborn 61-wicket stand after 10 balls on the day was finally broken when Nathan Lyon was bowled by Jasprit Bumrah for 41.
Last man Scott Boland scored a hard-hitting 15 off 74 balls.
Bumrah took an exceptional 5-57 to give the fast bowler nine Test wickets and 30 across the first four Tests of the series.
DJI/DH