Australia set South Africa 376 runs to win the third Test in Sydney on Tuesday.
26 overs remain on day four with a full day's play to follow on Wednesday on an SCG pitch starting to keep low.
Opener Simon Katich top-scored with 61 on his home ground and Ponting made 53.
First-innings century-maker Michael Clarke was last man out for 41 caught in the deep off the bowling of spinner Paul Harris after the NSW batsman appeared to suffer a minor leg-muscle strain earlier in his innings.
Mike Hussey was unbeaten on 45, hitting one massive six over long on and 10 rows back into the Bradman Stand.
Ponting declared as soon as Clarke was out at 4pm (AEDT), 90 minutes before the scheduled close of play.
South Africa are likely to be batting one short with skipper Graeme Smith nursing a cast on his fractured left hand after retiring hurt for 30 in his side's first innings.
Australia's under-siege opener Matthew Hayden fell for 39 in the morning session, departing to respectful applause from the crowd who wondered if the 103-Test veteran had played his last innings.
The Queensland left-hander was bowled by Morne Morkel after hitting seven fours in a better display than his first-innings 31.
Hayden has scored only 383 runs at 23.93 in his past nine matches since recovering from an Achilles injury. The 37-year-old has an impressive overall record of 8625 runs at 50.73 but has contributed only 117 runs at 19.56 in this series.
Ponting was also bowled by Morkel (2-38) after lunch, facing just 57 balls and dominating a second-wicket partnership of 72 with Katich.
Paceman Dale Steyn, battling a bruised heel, ended Katich's 222-minute stay with a successful lbw appeal at 3-181.
Australia trail 2-0 in the three-match series and need a victory in the dead-rubber match to avoid a whitewash and maintain top ranking in the Test championship.
The highest successful fourth-innings chase in a Sydney Test was Australia's 2-288 against South Africa three years ago.
Peter Siddle's career-best figures of 5-59 helped Australia bowl the Proteas out for 327 on Monday in reply to the home side's 445.