Centuries from Lokesh Rahul (110) and Virat Kohli (batting 140) held the Indian innings together, ending the third day's play at 342 for five, still trailing Australia by 230 runs in the fourth and final Test at the Sydney Cricket Ground (SCG) here Thursday.
Resuming at 71 for one, India put on 271 runs in 90 overs on the third day but a couple of wickets in the last session put them in a sticky situation.
Kohli and company will need to grind it out in the first couple of hours Friday if they are to get close to Australia's mammoth first innings total of 572 for seven declared.
Some tight bowling in the morning helped Australia restrict India to score only 51 runs in 30 overs in the first session of play. The visitors started cautiously but made sure they did not lose wickets.
Rohit Sharma (53) scored some runs as he reached his first half-century of the series. However, immediately after reaching fifty he attempted a sweep off the bowling of spinner Nathan Lyon, only to misjudge the ball and be castled.
However, thereon Kohli and Rahul struck a vital 141-run third wicket partnership which steadied the ship for India. Coming out post-lunch at 122 for two, the second session entirely belonged to India as the visitors scored 112 runs in 30 overs without losing a single wicket.
Rahul, 22, scored his maiden century in only his second Test after a disastrous debut in Melbourne where he had scores of 1 and 3.
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However, he rose from that failure and played a patient yet composed innings to reach his century in 253 balls. His knock was highlighted by 12 boundaries and one splendid six over deep mid-wicket.
The Bangalore boy heaved a sigh of relief after reaching his century and became a little loose with his shots. This had an immediate impact as he top edged a bouncer soon after tea only to be caught and bowled by Mitchell Starc (2/77).
In the meantime, Kohli solidified his innings to score his fourth century of the series and 10th of his career. His innings of 140 not out, laden with 20 boundaries, also broke the record for most runs by an Indian in a series Down Under, going past the ever-reliable Rahul Dravid's 619 runs scored in 2003-04 series.
In the process, the Delhi lad also became the first ever player to score three tons in the first three innings as a skipper.
Just when it looked like India could end the day in a strong position, all-rounder Shane Watson (2/42) clinched Ajinkya Rahane (13) and Suresh Raina (0) on successive deliveries.
Playing a Test match after almost two and a half years, Raina failed to make an impact as he followed a slow and swinging delivery only to edge it and get caught behind.
India ended the day with wicketkeeper-batsman Wriddhiman Saha (batting 14) striking an unbeaten 50-run stand with Virat Kohli.
The most successful bowler of the series with 20 wickets, Lyon (1/91) looked lethal with the old ball on a turning track but had to be content with the lone scalp of Rohit Sharma.
Australian bowlers tried their best to take more wickets but they were, uncharacteristically, not supported by their fielding.
Rahul was lucky on two occasions. Australia had a brilliant chance of running him out just after Rohit's dismissal which they totally messed up.
Rahul had another escape when he was dropped by Australia skipper Steven Smith, who ran back from slip to catch a top edged pull. The ball eventually burst through his hands into the ground.
Later, Smith also dropped Kohli just before tea at second slip.