Adam Ashley-Cooper and James O'Connor scored tries for the home side, with Matt Giteau adding two penalties and a drop goal as the Wallabies secured their opening win of the campaign.
Morne Steyn, the hero of South Africa's summer triumph over the Lions, replied with a brace of penalties for the Boks but the world champions failed to build on last weekend's impressive victory over the same opposition.
The result was the first loss for the Boks since their third-Test reverse to the Lions on July 4 and was the first blemish on their 2009 Tri Nations record.
That defeat now means the All Blacks can still win the southern hemisphere's most prestigious tournament for the fifth year in a row.
But Graham Henry's men will only do so if they can prevent the Boks from picking up a bonus point in defeat when the two teams clash next Saturday and then beat the Wallabies a week later.
New Zealand are at home in both fixtures but their task is made even harder by the fact that they must pick up at least one try-scoring bonus point from the two games and turn around a 39-point deficit to the Springboks in the points for and against chart.