Kyle Abbott picked up the first wicket of the day by dismissing Usman Khawaja.
Kyle Abbott thought he had the wicket of Steven Smith, but DRS came to the aid of the Australian captain.
Australia suffered their fifth straight Test loss and also their first series defeat at home in four years.
Peter Nevill, Joe Mennie and Steven Smith all fell to Kagiso Rabada, who picked up a four-wicket haul in the second innings.
Kyle Abbott picked up nine wickets in the game, including a six-wicket haul in the second innings to power South Africa to a victory by an innings & 80 runs.
Kagiso Rabada sent back Callum Ferguson to leave Australia in more trouble.
This was South Africa's third straight series win in Australia.
Adam Voges's poor form continued as he fell to Kyle Abbott.