Lokesh Rahul hit his maiden century, Virat Kohli his fourth of the series but Australia's Shane Watson hit back with two wickets in as many balls to leave India on 342 for five after the third day of the fourth test on Thursday.
Kohli, who became the first player to score centuries in his first three innings as test captain, was still at the crease on 140 when stumps were drawn after a hot, sunny day packed with incident at the Sydney Cricket Ground.
India, already 2-0 down in the four-match series, had resumed on 71-1 in reply to Australia's 572-7 declared and restored a great deal of pride as well as reducing the deficit to 230 runs.
Rahul had more to prove than most after his torrid introduction to test cricket in Melbourne last week, where he scored four runs in two innings.
The 22-year-old rode his luck and was forced to dive bat-less into the Sydney dirt to prevent being run out soon after Rohit Sharma (53) had become the only batsman to fall in the opening session.
He was perhaps even more fortunate to escape with his wicket just before lunch when, on 46, he ballooned the ball into the air but Steve Smith failed to hold the catch.
The Australian captain, who later also dropped Kohli on 59 at second slip, made it clear he believed the wire that holds the overhead TV camera — Spidercam — in place had prevented him from dismissing Rahul.
Rahul and Kohli batted cautiously through the second session in a partnership of 141, the opener reaching the century mark with his 11th four just before tea having faced 253 balls.
He was gone soon after the break for 110 when he skied another pull shot to be caught and bowled by paceman Mitchell Starc but his captain soon joined him as a Sydney centurion with a drive down the ground for two runs.
Kohli, who scored a century in each innings in Adelaide and another in Melbourne, joined English batsmen of the 1920s Wally Hammond and Herbert Sutcliffe as the only visiting players to have scored four centuries in a series in Australia.
Indian cricket fans have become used to batting collapses over the last year, however, and all-rounder Watson roused the crowd by dismissing Ajinkya Rahane (13) and Suresh Raina in consecutive balls.
Wriddhiman Saha held firm to prevent Watson's hat-trick and will resume with Kohli unbeaten on 14 on Friday.