South Africa, set a target of 410, were 29 for no wicket at close when bad light ended play early 13 balls after tea on the fourth day.
Australia had declared their second innings on 307 for four after Ponting added 116 to the 103 he made in the first innings.
He now has 30 Test centuries to his credit, one more than Bradman, and is only the second man after India's Sunil Gavaskar to score centuries in each innings of a Test three times.
While Gavaskar first achieved the feat in 1970-71 and did so for the third time in 1978-79, all of Ponting's twin century matches have come this season.
Today's ton was his fifth in his last eight innings against South Africa.
Australia resumed on 125 for one and Matthew Hayden and Ponting took their second-wicket stand to 201 before they were separated in the eighth over after lunch.
Ponting reached his century with a push to mid-on for a single off Makhaya Ntini, whose next ball was a wide delivery that Hayden drove at and edged to wicketkeeper Mark Boucher.
Hayden scored a measured 102 off 217 balls with 12 fours.
Ponting, who faced 187 balls and hit 12 fours and two sixes, was out nine overs later when he top-edged a pull shot to a ball from seamer Shaun Pollock and was caught at deep square leg.
South Africa faced 7.1 overs before play was called off for the day with AB de Villiers on 17 and Graeme Smith on 10.
Australia won the first Test of the three-match series by seven wickets.