India need 70 runs to level the Border-Gavaskar series after dismissing Australia for 200 in the Boxing Day Test at the MCG.
The hosts survived the entire first session of day four, but India took the extra half hour on offer with only one wicket left to claim and completed the job with a minute to spare.
Bowlers Mitchell Starc and Josh Hazlewood almost got to lunch but spinner Ravi Ashwin bowled the latter for 10 for his second wicket.
Australia's lower-order, spearheaded by young allrounder Cameron Green, added 67 runs on Tuesday after resuming on 6-133
But Green's dismissal for an innings-high of 45 left only the tail to try to set India a defendable run-chase.
Playing in just his second Test, Green lasted for most of the session to frustrate India's bid to level the series at one-all.
His promising innings ended when he mistimed a pull shot off Indian debutant Mohammed Siraj, who finished with figures of 3-37.
The West Australian received solid support from fast bowlers Mitchell Starc and Pat Cummins.
Despite Green's disappointing dismissal, he showed enough to see why Greg Chappell has labelled him Australia's most talented batsman since Ricky Ponting.
He displayed poise that most of his more experienced teammates failed to show during the day-three batting collapse.
Green's 146-ball stay was the most deliveries an Australian batsmen has faced in one innings during this series.
Starc survived multiple close calls, including one review where he almost walked off the field, to be unbeaten on 14.
Cummins was also resilient, as he survived for 103 balls before the vice-captain fell to Indian quick Jasprit Bumrah for 22.
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