Veteran batsmen Rohit Sharma and Virat Kohli fell cheaply Monday as India were reduced to 33-3 at lunch, leaving Australia two sessions to wrap up a victory in the fourth Test.
An unrelenting Pat Cummins took 2-10 off nine overs, removing Rohit for nine and KL Rahul for a duck in quick succession on the fifth morning at the Melbourne Cricket Ground.
India's hopes of reaching their target of 340 then suffered a further blow when Kohli departed off the final ball before the interval.
Kohil had scored just five when he tried to drive a wide delivery from Mitchell Starc and edged to Usman Khawaja at first slip.
Opener Yashasvi Jaiswal was 14 not out at the break after grinding for 83 balls, while India's run rate reduced to a stagnant 1.26 by accurate Australian bowling.
India need a record fourth-innings Melbourne run chase of 340 to go 2-1 up in the series, after Australia posted 234 in their second innings.
They will most probably need to bat out the rest of the day to save a draw and push the series to 1-1 ahead of the last Test at Sydney, starting on Friday.
Australia captain Cummins extended a remarkable Test with bat after scoring 49 and 41 with it and then broke a double wicket-maiden over in the 17th over.
Opposing skipper Rohit had batted with discipline but fell when attempting an aggressive whip across the line that flew quickly to Mitchell Marsh at gully.
The out-of-form Rohit has failed to go past 10 in three Tests after missing the opener in Perth for the birth of his second child.
India were 25-1 by then and it soon was 25-2 as Rahul went five balls later, playing a rising Cummins delivery to Khawaja at first slip.
Earlier, the stubborn final-wicket stand of 61 by Australia finally broke 10 balls into the day when Nathan Lyon was bowled by Jasprit Bumrah for 41.
Tailender Scott Boland compiled a dogged not out on 15 off 74 balls.
Marnus Labuschagne top scored for the home side on Sunday with 70, helping to revive an innings that was faltering at 91-6.
The exceptional Bumrah took 5-57 to give the fast bowler nine wickets for the Test and 30 across the first four Tests of the series.
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