One down in the four-match series, the tourists struggled to 83 for four in the first session, but Matthew Wade and captain Michael Clarke ensured they did not lose a wicket in the second, putting on 124 for the fifth wicket.
Clarke went into the tea break unbeaten on 68 from 132 balls, while wicketkeeper Wade was 55 from 119.
After the visitors won the toss, Bhuvneshwar Kumar bowled David Warner (Six) with a delivery which cut back into the left-hander, then trapped Ed Cowan (four) lbw with a ball which may have pitched outside leg stump.
That left Australia 15 for two, with Phillip Hughes and Shane Watson at the crease.
The pair effected a mini-recovery, with the left hander playing some eye-catching late drives off the back foot, but Watson (23) then fell lbw attempting to to a ball which kept a little low with the score on 57.
Hughes (19) followed, caught behind at the second attempt by Mahendra Singh Dhoni off the bowling of Ravichandran Ashwin, before Wade and Clarke began the Australian recovery.
After facing 95 balls, Clarke brought up his 26th Test half century with a single in the 48th over, edging his side closer towards 150.
On 52 India missed their best opportunity to dismiss Clarke as the skipper inside edged on his pad with the ball dropping to a diving Cheteshwar Pujara who got his fingers under the ball, but could not hang on.
Wade reached his half-century in the 55th over as Australia batted themselves back into the game.