The away side took an early lead as Coenraad Oosthuizen touched down and Morne Steyn converted.
Christian Leali'ifano's two penalties reduced the deficit but South Africa were soon 13-6 ahead as Steyn kicked over twice.
The Boks continued to have the better of the match towards the break and moved 10 points in front as Steyn notched his third penalty of the day.
The home Brisbane crowd were left frustrated when the Wallabies opted to go for touch rather than take a penalty try.
Leali'ifano struck his third and fourth penalties early in the second half, but the Boks again fought back as Jean de Villiers went over. However Steyn's kicking let him down for once as he hooked the conversion wide.
The result means that Australia are bottom of the table.