Ponting, the third all-time highest Test runscorer behind Indians Sachin Tendulkar (15,432) and Rahul Dravid (13,262), batted throughout the middle session with Clarke to recover the home side after the loss of three morning wickets.
At tea, Australia were 214 for three after winning the toss with Ponting unbeaten on 91 and Clarke on 71.
India, looking to restore some pride after drubbings in the first three Tests, were thwarted by the pair's unbroken 130-run stand for the fourth wicket on a flat batting strip.
Clarke, who scored an unbeaten 329 in the second Sydney Test earlier this month, had a life on 50 when Dravid put down a low chance off Ishant Sharma.
Adelaide Oval is a happy hunting ground for former skipper Ponting, who has scored five of his 40 Test hundreds there including a knock of 242.
The tourists claimed the wickets of David Warner (8) and Shaun Marsh (3) cheaply in the opening 10 overs and Ed Cowan (30) nearing lunch.
Warner, who smashed a 69-ball century on the way to a swashbuckling 180 in the third Perth Test win, only lasted 23 balls before he was trapped leg before wicket by Zaheer Khan.
He was followed by the imperilled Marsh, who again fell cheaply, lasting only 12 balls when he was bowled by a straightened delivery from off-spinner Ravi Ashwin.
Marsh did nothing to dispel doubts over his Test career with just 17 runs in five innings in the series batting at number three.
Cowan looked to have got set before he was caught low down in the covers by VVS Laxman for Ashwin's second wicket 10 minutes before lunch.
Stand-in skipper Virender Sehwag was proactive with his bowling changes in the morning session, wheeling in Ashwin in the fourth over of the innings and rewarded with Marsh's wicket in Ashwin's fourth over.
Sehwag also bowled his offbreaks in tandem with Ashwin in the first session of the Test.
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Yes. I agree with you zezu. But, till last ball we can't say something. Otherwise, it's a remarkable achievement by Ponting.
Looks like another humiliating defeat on the cards!!