Australian fast bowler Pat Cummins claimed four wickets to dent India's reply but Cheteshwar Pujara's unbeaten century left the third Test evenly poised in Ranchi on Saturday.
India were 360 for six at stumps on day three, still trailing the visitors by 91 runs in their first innings. Pujara (130) and Wriddhiman Saha (18) were batting at close of play.
Cummins, making a return after playing his only Test for Australia in 2011, got crucial breaks including the prized scalp of India skipper Virat Kohli.
The 23-year-old Cummins was ably supported by fellow paceman Josh Hazlewood and spinner Steve O'Keefe who took a wicket each on pitch that still looked good for batting.
Pujara, who was involved in a 102-run second-wicket stand with overnight partner Murali Vijay (82), was holding the innings together with his 11th Test century.
Pujara hit 17 boundaries, in an otherwise sedate knock, to keep India's hopes alive of surpassing Australia's first innings total of 451.
"I think the game is evenly poised. If we can get closer to the target and possibly extend the lead from there, I think it's going to be a good game on hand," Vijay told reporters.
"Pujara was rock solid, hopefully he can put up a great show for us tomorrow. Definitely run scoring was difficult, they too bowled on very good areas," said Vijay.
Pujara built crucial partnerships with Ajinkya Rahane (14) and Karun Nair (23) but the Australian pacemen rattled India's middle order with some inspired bowling.
Cummins, who struck twice in the afternoon session, got Rahane caught behind and Hazlewood bowled Nair with a beautiful reverse swinging delivery in the final session.
"I thought last night he (Cummins) bowled particularly well but today he backed that up. To produce some of the balls that he produced to get wickets was exciting," said Australia's assistant coach David Saker.
"Hats off to selectors to go with him. Ball speed in India is a big thing because the wickets don't generate any pace...we know what sort of a talent he has but it was so pleasing to see him do well."
Australia skipper Steve Smith kept up the pressure by rotating his bowling options as runs trickled in for the hosts in the final two hours of play.
India, whose innings run-rate is less than three an over, managed to score only 57 runs in the 31 overs bowled in the final session and lost two wickets.
- Kohli's prized scalp -
Earlier Kohli, who turned out to bat at his regular number four spot laying to rest any injury concerns, lasted only 23 balls before edging a catch to his opposite number Steve Smith at second slip.
The star batsman had injured his right shoulder after an awkward fall while fielding during Australia's innings on Thursday and stayed off the field for 400 minutes before taking crease.
Kohli, who came into the rubber with double centuries in four successive series, has only managed 46 runs in his five innings since the opener in Pune.
"Very satisfying seeing Kohli out cheaply...At the moment we have got the better of him but we know such a good player can bounce back at any time," said Saker, who added that the ongoing game is "evenly poised".
In the morning session, Vijay hit a gutsy 82 before undoing his hard work by being stumped off O'Keefe at the stroke of lunch.
The series between the world's top two sides is hanging at 1-1 with India needing at least a draw to have any chance of winning back the Border-Gavaskar Trophy.