Pakistan started well in the final Test of the three-match series, pegging Australia back to 80-3 at lunch.
But having been dropped when still on nought, Ponting ended the day on 137 to hit only his second Test century on his home ground at Bellerive Oval.
The veteran Aussie skipper ended a run of shaky form to put on an unbroken 231 in 69.4 overs with Clarke.
Australia have an unassailable 2-0 lead in the three-match series, but things looked promising for the tourists in the opening session when, having lost the toss, they claimed the wickets of Simon Katich, Shane Watson and Mike Hussey.
Katich was the first to go, departing in the seventh over for 11 after being adjudged lbw on referral off Mohammad Asif.
Ponting should have followed without scoring when he was also tempted into a hook shot by Asif and skied the ball straight to young paceman Mohammad Aamer at fine leg. Aamer did not have to move, but elected to take the ball at waist level rather than at head height. He lost sight of the ball and spilled the catch.
The visitors made some amends with the dismissal of Watson for 29 when he cut Umar Gul straight to Imran Farhat at gully, and Australia were under even more pressure when Aamer had Hussey caught behind by Test debutant Sarfraz Ahmed for six.
But Ponting then dispelled all criticism about his form as he took centre stage with Clarke.
His 39th Test century arrived in 159 balls with 13 fours with Clarke ably partnering him, reaching his 13th Test ton from 188 balls to end the day unbeaten on 111.
Asked for his thoughts when his hook sailed towards Aamer, Ponting said: “I was thinking about having a long day in the change rooms with not much to do and what paper I was going to read.
“When you hit one like that it feels like it hangs forever and I said to ‘Pup’ (vice-captain Michael Clarke) that it was probably too easy a catch because he didn’t have to move at all.
“He didn’t have to take a step but thankfully he put it down and it gave me another opportunity and 70 or 80 overs later I am still out there.”
Questioned further about his use of the hook he said: “It’s always been one of the shots I have naturally played.
“Pup asked me, ‘have you thought about not playing it?’, but I can’t because it’s just an instinctive thing. I don’t look at it as being a statement shot – it’s just one of those shots that is more natural to me than most.”
The skipper added that the Bellerive surface was another factor in his difficulty with the stroke.
“I struggled with it early on because I wasn’t watching the ball closely enough,” he explained.
“And with the wicket being a little bit on the slow side and the ball holding up on the surface it was even harder to play that shot earlier on, but the longer I was out there I started to play it better and I picked up a couple of boundaries.”
