Opener Shikhar Dhawan made the fastest debut hundred in Test history as India raced to 283-0 in reply Australia's first innings of 408 by stumps on day three in Chandigarh.
Dhawan, who was called in to replace the out-of-form Virender Sehwag for the third Test, reached three figures from 85 balls and went on to finish unbeaten on 185 from 168 deliveries.
Murali Vijay played a supporting role and was 83 not out by the close, by which time India had reduced their deficit to 125.
The stand was a record opening partnership at the PCA Stadium and Dhawan's innings - which has contained 33 fours and two sixes so far - is already the highest by an Indian on debut, beating Gundappa Viswanath's 137 in 1969.
Dhawan's effort overshadowed the good work done by Australia's lower order earlier in the day.
On 273-7 overnight, Steve Smith and Mitchell Starc extended their eighth-wicket stand to 97 but both missed out on maiden Test centuries.
Starc falls for 99
Smith was stumped off the bowling of left-arm spinner Pragyan Ojha (2-98) for 92, while Starc - whose previous best first-class score was 68 - fell on 99, edging a delivery from Ishant Sharma (3-72) through to wicketkeeper Mahendra Singh Dhoni.
Australia trail 2-0 in the four-match series and are without four players - Usman Khawaja, Mitchell Johnson, James Pattinson and Shane Watson - for disciplinary reasons.
The quartet were not considered for selection after failing to complete a feedback assignment from coach Mickey Arthur.
Watson, the vice-captain, has since returned home for the birth of his first child and it is unclear if he will return for the final Test after saying he was considering his future.