Skipper Rohit Sharma hit a brave 120 on a turning Nagpur pitch as India extended their lead to 144 despite Australian debutant Todd Murphy's five wickets in the opening Test on Friday.
India were 321-7 at stumps with all-rounder Ravindra Jadeja proving his worth for the second straight day of his international return with an unbeaten 66.
The 22-year-old Murphy took regular wickets with his off-spin in his attempt to check India's surge but Jadeja kept up the charge following Rohit's dismissal soon after tea.
Jadeja was batting alongside fellow left-hander Axar Patel, who hit 52, as the pair put on an unbeaten stand of 81 for the eighth wicket.
Rohit led from the front with his ninth Test century to extend India's dominance after they dismissed Australia for 177 on day one of the four-Test series.
The captain defied the spinners to reach his hundred with a boundary off Murphy in the second session, and took off his helmet to soak in the applause.
He put on a key 61-run sixth-wicket stand with Jadeja, who stood firm after Rohit's departure to register a fifty after his five wickets in the Australian innings.
Jadeja, who has three Test hundreds, did his trademark sword swish with the bat to mark his 18th half-century in the five-day format.
Murphy stood out for the tourists with remarkable control to knock off the stalwarts of Indian cricket including Virat Kohli, caught behind for 12.
Murphy, who claimed KL Rahul as his first Test wicket on Thursday, trapped Ravichandran Ashwin lbw and got Cheteshwar Pujara caught at short fine leg in the first session.
Senior Australia spinner Nathan Lyon spoiled Twenty20 sensation Suryakumar Yadav's Test debut after he bowled the batsman on eight to put India in a spot at 168-5.
But Rohit, who started the day on his overnight 56 and smashed Pat Cummins and Lyon for a six each, and Jadeja soon swung back the momentum with a mix of caution and aggression.
Cummins took the second new ball after tea to send back Rohit bowled, one ball after he was dropped by Steve Smith at second slip.
Murphy soon bagged his fifth as he trapped fellow debutant Srikar Bharat lbw -- a decision that was given not out by the umpire but successfully reviewed by Australia.
Jadeja, who returned from a knee injury with a 5-47 on Thursday, soldiered on with Patel as they frustrated the opposition attack in the final hour of play.
Axar smashed eight boundaries en route to his second Test fifty.
