Steve Smith's unbeaten 178 and a maiden Test century for Glenn Maxwell boosted Australia to a competitive total but India responded well in Ranchi.
Smith recorded his best score in Asia and his masterful innings, along with Maxwell's 104, lifted the tourists to 451 all out on day two of the third Test, with Ravindra Jadeja finishing as the pick of the bowlers with five for 124.
India, in response, closed on 120 for one as Pat Cummins marked his return to Test cricket with the wicket of KL Rahul, who feathered behind to depart for a well-crafted 67.
Rahul had been the aggressor in a 91-run opening stand although he and Murali Vijay, back in the team for his 50th Test after missing out in Bangalore because of a shoulder injury, did not take many risks.
Rahul brought up his fourth fifty in five innings although once again he could not convert as he nicked behind to Matthew Wade to give Cummins his first Test wicket since November 2011.
Cummins' express pace in only his second Test gave the Indian batsmen pause for thought but he could not make another breakthrough as Vijay (42no) and Cheteshwar Pujara (10no) survived to the close.
Their efforts gave India captain Virat Kohli another night to rest a shoulder injury he sustained while diving to prevent a boundary on the opening day.
He did not take to the field on Friday morning as opposite number Smith, a centurion on Thursday, and Maxwell set about swelling Australia's total, resuming on 299 for four.
After seeing his bat break off the first ball of the morning, Maxwell survived a couple of nervy moments to bring up three figures, reaching the landmark with a slash between two slips that flew away for his ninth four.
Maxwell was dismissed three overs later, though, ending a 191-run partnership with Smith, after edging behind off Jadeja, who saw off Wade in an identical manner after a quickfire 37 before bowling Cummins two balls later.
Smith remained untroubled, however, effortlessly moving to his 150 and he received capable support from Steve O'Keefe (25) to take Australia well beyond 400.
Jadeja had his fifth when Lyon fended to silly point while the slow left armer executed a superb 'no-look' run out of Josh Hazlewood to end Australia's innings as Smith, who struck 17 fours in his 361-ball knock, was denied the chance of reaching his double century.