Hayden, hit 10 fours and a six in his 112-ball 59 for his highest score in the series so far.
At the break, captain Ricky Ponting was batting on 14 with the left-handed opening batsman.
Replying to India's mammoth 613-7 declared, Australia were off to a steady start with Hayden and Simon Katich (64) playing cautiously on a track that showed promise for spinners.
Katich looked fluent in his strokeplay, hitting 10 fours and completing his 10th Test fifty in the process.
Three times he hit Indian paceman Ishant Sharma for four and appeared at ease against the leg-spin of veteran Anil Kumble, who has conceded 40 runs off his 11 overs so far.
Katich was undone by Kumble's spin partner Amit Mishra who lured him into playing a flick from outside the off stump and then watched as the ball sneaked through the gap and knocked off the middle stump.
Indian pace spearhead Zaheer Khan, who started the morning with two bouncers to Hayden, failed to get an early breakthrough for the hosts this time.
Hayden looked determined to end a poor run of scores, having hit 0, 13, 0 and 29 in the two Tests, and played each ball on its merit.
The burly Queenslander pulled Mishra over mid-wicket for a huge six to bring up Australia's 100 in the 29th over, completing his 28th Test half-ton in the process.
India lead the four-Test series 1-0 after winning the previous match in Mohali by 320 runs.
The fourth and final Test will be played in Nagpur from Nov 6-10.