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According to the supersport.com website, Steven Smith was unbeaten on 58 - his third Test half-century - and Mitchell Starc had 20.
The hosts kept pegging away at the wickets after tea, first snaring Ed
Cowan for a hard-fought 86 as Ravichandran Ashwin got rewarded for some
superb bowling during the day.
He tossed one up, which dipped on Cowen who edged it to Virat Kohli in the slips. His innings lasted 238 balls and included eight fours.
Three quick scalps followed, putting Australia firmly on the back foot, when Ishant Sharma removed Brad Haddin (21) and Moises Henriques (0) in the same over.
Ravindra Jadeja soon added to his two earlier successes by trapping Peter Siddle for the visitors' third duck of the innings.
After a solid 139-run opening stand between Ed Cowan and David Warner - Australia's first 100-run partnership of the series where Michael Clarke was not involved - India retaliated with three quick wickets after lunch to have Australia on 180 for three at tea.
Cowan (76 not out) was the stabilising factor, and together with Smith (19 not out) they stopped the rot after India's spinners put the brake on Australia's top-order.
Jadeja struck first when he found the inside edge of David Warner's bat when he had 71, and the ball hit the top of his pad to lob to Mahendra Singh Dhoni behind the stumps for an easy catch.
Australia's run machine, Michael Clarke, retraced his steps to the pavilion the very next ball when Jadeja ripped an off-break around Clarke's bat, dragged him out of his crease and Dhoni completed a quick stumping.
Phil Hughes survived for 31 deliveries before Prayan Ojha turned and bounced one down leg that caught the hapless batsman's gloves and Dhoni mopped up the chance. This ended Hughes's miserable time against spin of late - dismissed five times, faced 70 deliveries and only scored two runs.
At lunch, Australia were 109 without loss after opting to bat.
Warner brought up his seventh Test-half-century in the over before the break, to leave the field unbeaten on 54 off 107 deliveries. Cowan had 43.
Australia made four changes to the team that lost the second Test, two of these were enforced by the suspension of four players following an internal disciplinary earlier this week.
Brad Haddin was brought back for Matthew Wade, Steven Smith replaces Shane Watson, Glenn Maxwell makes way for Nathan Lyon and Mitchell Starc takes James Pattinson's place.
India drafted in debutant and left-hand batsman, Shikhar Dhawan, after Virender Sehwag was axed from the team, and Pragyan Ojhan comes in for Harbhajan Singh.
After losing the whole of the first day due to rain, all subsequent days will start 30 minutes early to make up some lost time. The follow-on difference has also been reduced to 150 instead of the normal 200 runs, because of the day lost.
