Booed to the crease by some Australian fans at Adelaide Oval, Indian captain Virat Kohli settled in style before falling to Nathan Lyon late on a rain-hit third day of the first Test.
The tourists boasted a 166-run lead at stumps on Saturday, having reached 3-151 in their second innings.
India's hopes of setting a match-winning target took a hit when Kohli was caught at bat-pad, more than an hour after what had been the scheduled time for stumps, but first-innings centurion Cheteshwar Pujara remained unbeaten on 40.
India will feel bullish as they hunt a 1-0 series lead and maiden Test series win in Australia, although momentum has shifted frequently and violently in the low-scoring contest.
Kohli and Pujara shared a cautious 71-run stand, the highest partnership in the match, as they attempted to bat the hosts out of the game.
The highest successful run chase in a Test at the venue is Australia's 6-315, achieved in 1902 against England, while no side has chased down more than 236 since the West Indies in 1982.
Kohli was typically animated in the morning session, celebrating jubilantly after India rolled Australia for 235 to claim a first-innings lead of 15 runs.
"You love seeing that passion in sport. Mind you, I think if we did that at the moment, we'd be the worst blokes in the world," Australian coach Justin Langer told Fox Cricket before the start of play.
Kohli, given a heated reception by some sections of the 30,348-strong crowd, ditched the histrionics when he walked out to bat with India 2-76 and the game in the balance.
The superstar misjudged a delivery that dipped late while on 34, having exhibited trademark composure during his previous 103 balls.
Lyon dismissed Pujara on eight and 17 but the batsman successfully used the Decision Review System (DRS) on both occasions to overturn umpire Nigel Llong's on-field verdict.
Lyon, with figures of 1-48 from 22 overs, shook his head in disbelief at the second reprieve.
KL Rahul and Murali Vijay saw off the new ball in a 63-run opening stand.