Prince was unbeaten on 79 when bad light ended play 11 overs early on Friday. Six other batsmen reached double figures but the next highest score was 37 by new South African captain Jacques Kallis.
Pressing for a clean sweep after clinching the series in the second Test in Durban, Australia had South Africa were in trouble at 106 for four when Kallis was bowled by a superb delivery from Brett Lee but Prince shared half-century stands with Jacques Rudolph (25) and Mark Boucher (24) as the home side made a partial recovery.
Prince made a century in the third Test against Australia in Sydney in January but has struggled in the home series against the world champions.
He made a slow start Friday before playing some polished strokes. His 79 was made off 128 balls with ten fours.
Stuart Clark was the most successful bowler in a disciplined seam attack, taking two for 61.
Australia named an unchanged team for the third successive match but South Africa were without regular captain Graeme Smith, who suffered an injured left ring finger during fielding practice Thursday. Kallis became South Africa's 31st Test captain.
Smith was diagnosed with a severe soft tissue injury and will wear a splint for 10 to 12 days.
Gibbs was promoted to open the batting with AB de Villiers, while Dippenaar batted at number three.
After a cautious start, De Villiers and Gibbs were dismissed within three overs of each other. De Villiers played a loose drive against Clark and was caught at cover for 12.
Gibbs left a ball from Michael Kasprowicz which cut back and hit his off stump. It was the eighth time in 11 Test innings that the out-of-form Gibbs had been bowled.
Dippenaar, in his first Test of the summer, looked solid as he and Kallis put on 59 for the third wicket but he played a loose shot against the accurate Clark and was caught behind for 31.
Kallis went when he played forward defensively against a ball from Lee which cut back at pace to bowl him off a faint inside edge and his pad.
Prince and Rudolph put on 55 for the fifth wicket before Rudolph was caught low down by Matthew Hayden at slip off Shane Warne. The decision was referred to square leg umpire Steve Bucknor who gave Rudolph out. Television replays were inconclusive as to whether the ball carried.
Boucher joined Prince in a 72-run stand for the sixth wicket before falling leg before wicket to Andrew Symonds nine balls before bad light stopped play.