Flying Springbok winger Bryan Habana scored two tries, one in each half, to prove the difference between the two teams.
South Africa-born Clyde Rathbone scored the Wallabies' only try 11 minutes into the second half which Mat Rogers converted.
Rogers also landed three penalties with Matt Giteau kicking a 14th-minute penalty but their efforts were not enough to stop the Springboks, whose last Test win over Australia in Perth was a 14-13 victory in 1998.
In 60 Tests between the two countries, South Africa have now won 38 times, with one draw - the 14-14 tie in Perth in 2001.
South Africa full-back Percy Montgomery was the match's leading points scorer with three first-half penalties and a 50th-minute drop goal. The Springboks led 14-6 at half-time.