India, playing for pride after losing the series with emphatic defeats in the first three tests, had removed Australia's top order before lunch but Ponting and Clarke have put on a huge fourth-wicket partnership to give the home side every chance of taking the series 4-0.
Ponting has compiled his 41st test century, and was 134 not out midway through the final session, with his successor as Australia captain Clarke on 131 not out on a sweltering day at the Adelaide Oval.
The 37-year-old Ponting, who scored his first century in two years in the second test in Sydney, brought up his 61st test fifty with two runs behind square leg just after lunch and scored his 13,000th test run with a swept single to deep square leg.
Clarke, who won the toss and elected to bat, has been in a rich vein of form himself and he reached his 19th test hundred soon after tea.
Virender Sehwag had made a good start as replacement skipper for the banned Mahendra Singh Dhoni, keeping the Australians on the back foot and bucking convention by introducing the off spin of recalled Ravi Ashwin in just the fourth over.
It was the pace bowling of Zaheer Khan at the other end, however, that forced the breakthrough when his inswinger trapped lefthander David Warner leg before for eight with just 26 runs showing on the picturesque ground's famous old scoreboard.
Shaun Marsh has had a poor series and that continued when Ashwin sent him back to the dressing room after 10 minutes, when the batsman completely misjudging the flight of a ball which went between bat and pad and took the bails off.
The 28-year-old's three runs took his tally to 17 in five innings in the series and he will need a big score if he gets to bat again to save his test career.
Ashwin struck again 10 minutes before lunch to remove Ed Cowan for 30, tempting the opener into a miscued cover drive that VVS Laxman intercepted with a fine low catch at short cover to leave Australia at 84 for three.
Sehwag's captaincy faltered, however, when Clarke, on 35, got a thick edge that would have been gobbled up by first slip only for the ball to fly through the huge gap between the wicketkeeper and second slip and go for four.
Dhoni was banned for one match by the International Cricket Council (ICC) after India failed to keep to an acceptable over rate in the third test.
