India's record second-wicket stand of 370 was finally broken by Australia as the home side reached 3-400 at lunch on day three of the second Test.
Murali Vijay (167) and Cheteshwar Pujara (204) had batted for over seven hours together but departed within six runs of each other on Monday in Hyderabad.
That left India leading by 163 runs with seven first-innings wickets in hand.
Test cricket's leading runscorer Sachin Tendulkar is unbeaten on three while Virat Kohli, who has made hundreds in his past two Tests against Australia, is four not out.
Vijay was caught at leg slip at 2-387 as debutant offspinner Glenn Maxwell claimed his first Test wicket.
Playing in his 14th Test, the opener Vijay struck 23 fours and two sixes in a knock that lasted seven minutes shy of eight hours.
Pujara, who completed his fourth hundred and second double-century in just his 11th Test, was out with the score on 393 after hooking a delivery from James Pattinson to fine leg.
Their partnership is a record for the second wicket for India in Test cricket and it's the third-highest by any country for any wicket against Australia.
Vijay and Pujara had been sailing towards a scoreline of 1-400 which would have given them the record stand against Australia of 383, beating England pair Len Hutton and Maurice Leyland who put on 382 at The Oval in 1938.
The 25-year-old young gun Pujara had looked out on 174 but left-arm spinner Xavier Doherty's lbw appeal was turned down by Sri Lankan umpire Kumar Dharmasena.
MS Dhoni's men lead the four-match series one-nil.