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Cape Town: South Africa were 404 for three at the close on second day, an imposing 195 runs ahead of Australia's first innings total of 209.
Prince, opening the batting for the first time in Test matches, made 150 while Kallis ended an 11-month century drought with unbeaten 102.
It put South Africa on track to secure a consolation win. Australia clinched the series by winning the first two Tests.
Controversy surrounded Prince's return to the South African side but the little left-hander seemed unruffled as he moved to his 11th Test century.
His hundred came up off 152 balls when he slammed leg-spinner Bryce McGain to the mid-off boundary. He exchanged handshakes with batting partner Kallis, who was named South African captain after Prince had initially been given the job.
Prince, a mainstay of the South African middle order over the last couple seasons before he was sidelined by injury, was their leader for the most of the day.
Taking a cue from the man he replaced as stand-in captain, Kallis weighed in with his 31st Test century.
He did the hard work last evening and this morning, seeing off the new ball, and forged stands of 65 with Imraan Khan, 97 with Hashim Amla, and 150 with captain.
Kallis made an awkward start, being struck twice on the body by Mitchell Johnson and on the helmet by Hilfenhaus in scoring his first two runs. He laboured to four off 39 balls before taking advantage of some loose bowling by McGain.
Brief Score: South Africa 404/3 (Prince 150, Kallis 102*) lead Australia 209 by 195 runs.
