Clarke batted through the day for his first test double century and the highest score by an Australian at the Sydney Cricket Ground, while Michael Hussey pitching in with 55 not out to give Australia a lead of 291 over India's first innings 191.
Ponting had departed just before tea for 134 to end the fourth-wicket partnership with Clarke at 288, a record for Australia in tests against India and a potentially match-winning effort from a pair who came together with the score on 37-3.
Needing victory to level the four-match series after a 122-run defeat in the opener in Melbourne last week, India's bowlers had been hoping for some early wickets but instead laboured all day in the heat.
Resuming the innings on 116-3, Clarke clipped a shot off his pads for three runs to bring up his fifty on the second ball of the morning and continued to play with composure as he moved towards his third century in his last six tests.
The 30-year-old reached his 18th test century, and the first of the series from either side, in the last over of the morning by slapping a Zaheer Khan delivery through the covers.
Ponting, who last scored a test century against Pakistan in Hobart in January 2010, matched his successor as captain almost run-for-run throughout the session but endured a nervous wait on 97 through the lunch break.
Three overs into the afternoon, however, the 37-year-old reached his 40th test century with a rushed single off the bowling of Ishant Sharma that could have cost him his wicket.
As Zaheer's throw at the stumps missed, Ponting was able to pick himself up, brush off the dust and take a standing ovation from the 30,000 crowd.
It was the first long period of dominance for the bat in a series where bowlers have had the upper hand and India's attack looked like journeymen until the new ball arrived.
Sharma finally broke up the partnership when he got some bounce into his deliveries and Ponting caught the ball high on the bat to give Sachin Tendulkar an easy catch in the gully.
By that time, Clarke had already reached his 150 and continued to hit the bowlers all over the ground to pass his previous best test score of 168 shortly before tea.
Sharma could have dismissed him caught and bowled on 182 but just failed to keep hold of the ball and Clarke reached his double century a couple of overs later.
The landmark arrived with two runs through square after 365 minutes, 284 balls and included 24 fours and a single six and Clarke celebrated wildly, running around the pitch swinging his bat in the air.
Hussey joined in the run-spree with some gusto and hit his 50 off 70 balls, reaching the mark an over after hitting two fours and a six in successive balls off spinner Ravi Ashwin.
It was undoubtedly Clarke's day, though. An authoritative cover drive saw him past Doug Walters' previous Australian record at the ground of 242 and there was still time to raise the 250.
India have never won a test series in Australia and face three days of hard work if they are to keep alive their hopes of doing so this year.
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