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.
However first-innings centurion Cheteshwar Pujara remains unbeaten on 40.
India 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.
"It's slightly in our favour ... we'll have a good lead if we capitalise tomorrow," paceman Jasprit Bumrah said.
Travis Head, who scored 72 to almost drag Australia to first-innings parity, described the match as evenly poised and backed his side to chase down anything.
Head, a former Indian Premier League teammate of Kohli's, didn't hear the heated reception from some sections of the 30,348-strong crowd.
"He's a pretty good player, he probably doesn't deserve to get booed," the South Australian said.
"Probably not needed but that's the crowd."
Ricky Ponting was disappointed to hear the boos, telling cricket.com.au it wouldn't have affected Kohli, while Bumrah played a straight bat by suggesting "as long as we're doing well we're happy".
Lyon broke a cautious 71-run stand between Kohli and Pujara, the highest partnership in the match, as the tourists attempted to bat Australia 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 West Indies in 1982.
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 shook his head in disbelief at the second reprieve.
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 ditched the histrionics when he walked out to bat with India 2-76 and the game in the balance, scoring 34 and largely exhibiting trademark composure.
KL Rahul, out for 44 after being offered a life by Aaron Finch on 32, and Murali Vijay saw off the new ball in a 63-run opening stand.
Their highest opening partnership outside India ended when the latter was removed for 18 by Mitchell Starc in similar fashion to day one.