Part-time offspinner Virender Sehwag broke through for his maiden five-wicket haul, but Clarke’s stout resistance in his knock of 112 meant it would be difficult for either side to manufacture a result on the final day.
The hosts took a 36-run lead when it dismissed Australia for 577 — its highest total in India — late in the afternoon, but lost Virender Sehwag and nightwatchman Ishant Sharma in reaching 43-2 at stumps.
Sehwag was bowled by Brett Lee for 16 before Sharma (1) popped a catch to Ricky Ponting in the next over from Stuart Clark. Gautam Gambhir was unbeaten on 21 at stumps while Rahul Dravid was on 5.
India leads the series 1-0 and would be unlikely to risk setting Australia a reachable target on the final day, meaning the series will probably be decided in the final test starting in Nagpur on Thursday.
Clarke, who struck six fours and a six in his 253-ball knock, was well supported by Cameron White as the pair batted through most of the middle session and combined for a 106-run stand for the seventh wicket.
White, who lifted Anil Kumble for a straight six, recorded his highest score in his three-test career with a valuable 44 from 95 deliveries before playing the ball onto his stumps while attempting a sweep off Sehwag just before tea, giving the Indian his fifth wicket.
Clarke was patient throughout a difficult innings and survived three chances, including one when he was missed at mid-off by Sharma before he had added to his overnight 21.
Another reprieve came on 91 when V.V.S Laxman spilled a simple opportunity from a top-edged sweep off Sehwag, who was also the unfortunate bowler in his next over, as Amit Mishra dropped a chance in the deep when Clarke was on 94.
He brought up his century with a cut for two through point from the ball before tea and after the break was ninth out after hitting Mishra to Zaheer Khan at long off.
Sehwag, who finished with 5-104, removed Matthew Hayden, Ricky Ponting and Michael Hussey on day three, and claimed another wicket on the fourth morning by bowling Shane Watson for 36. His previous best figures of 3-12 came against South Africa in Kanpur in April.
Watson and Clarke negotiated the first hour after the pair resumed at 338-4. Their 73-run partnership for the fifth wicket ended when Watson moved too far across the stumps and was bowled by Sehwag.
Sehwag took on a heavier bowling load on Friday after captain Kumble was forced to get treatment for a split webbing on his left hand.
Kumble, who required stitches for the wound and wore a large bandage, returned to bowl in Saturday’s opening session and took his first wicket of the series when he had wicketkeeper Brad Haddin stumped for 17, leaving Australia at 426-6.
Lee became Kumble’s second victim, falling lbw for 8 after trying to sweep, and he took a fine running catch to remove Mitchell Johnson caught-and-bowled to end the inning. Kumble finished with figures of 3-112.
Australia’s total of 577 bettered its 574-7 declared in Chennai in 1986, and was its second highest in all tests against India, behind the match in Adelaide in 1948.