According to the supersport.com website, Clarke was unbeaten on 103 - his sixth ton against India and third in India - as he held up his end while Ravichandran Ashwin wreaked havoc at the other.
Aswin finished the day with 6-88, adding that of Moises Henriques for 68 in the evening session, before Ravindra Jadeja got rid of Mitchell Starc before close.
Earlier, Ashwin took another three wickets to reduce Australia to 215 for five at tea after the visitors won the toss.
Both Shane Watson and David Warner fell soon after the lunch break for 28 and 59 respectively.
Ashwin deceived Watson with a shorter ball that kept low and trapped him in the crease, while Warner - who continued playing back to the fuller one - also fell victim to the spinner and was wrapped on the pads in front.
Matthew Wade only made 12 before handing Ashwin his fifth wicket of the innings, playing down the wrong line and also adjudged leg-before.
When the players left the field for tea, captain Michael Clarke was on 45 and debutant Moises Henriques had 29.
Earlier, Australia went to lunch on 126 for two.
The visitors saw off the new ball, with Ed Cowan and Warner adding 64 runs for the first wicket.
However, Warner did survive a few chances when first he was dropped by Virender Sehwag off Ashwin at first slip when he had 18, reminiscent of the dropped catch that gave Alastair Cook a life in Mumbai - also off Ashwin.
Cook went on to make a century, and England won that match by 10 wickets.
Two overs later, Ashwin was denied Warner's scalp again, with a ball that turned and dipped. Warner drove at it, dragging his foot out of his crease, but Mahendra Singh Dhoni was undone by the bounce and failed to remove the bails.
Warner had 27 at the time.
Nonetheless, in the 15th over, Cowan (29) was undone by Ashwin as he attempted to hit him out of the ground. Dhoni made amends when he collected this delivery in front of his chest to complete the stumping.
Phil Hughes fell shortly thereafter, playing a short, turning ball from Ashwin onto his stumps for six.
At the break, Warner had 58 - his sixth Test half-century - and Watson was on 28.
Earlier, Harbhajan Singh became only the 10th Indian player to play 100 Test matches, on a pitch that is looking dry and flat.
The hosts have favoured Ravindra Jadeja over Ajinkya Rahane, while Bhuvneshwar Kumar has been given his Test debut.
Teams:
India: V Sehwag, M Vijay, CA Pujara, SR Tendulkar, V Kohli, RA Jadeja, MS Dhoni (capt & wk), R Ashwin, Harbhajan Singh, B Kumar, I Sharma
Australia: DA Warner, EJM Cowan, PJ Hughes, SR Watson, MJ Clarke (capt), MS Wade (wk), MC Henriques, PM Siddle, MA Starc, JL Pattinson, NM Lyon