Proteas skipper AB de Villiers had vowed his side would be seeking redemption after being beaten by 32 runs in the series opener on Friday.
His team backed those words with a superb bowling display as the home side were dismissed for just 154 in 41.4 overs on what appeared a good batting wicket.
South Africa overcame some anxious moments and reckless batting to edge to the victory target, reaching 157 for seven in just 27.4 overs.
Towering paceman Morne Morkel led the way for South Africa with 5-21, his second five-wicket haul in one-day internationals and career-best figures in a man-of-the-match performance.
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Morkel said the South Africans were much better with the ball on Sunday, after conceding 300 runs on Friday.
"We put them under pressure more today," he said.
"On this wicket you need to go a touch fuller.
It's always nice when the ball is carrying and the keeper is catching it head high, but you are actually just wasting energy.
By contrast, stand-in Australian captain George Bailey was less than impressed with his side's batting.
"There were probably not that many dismissals where guys would say that ball was too good, but it was a culmination of South Africa building pressure and our batters exploding a bit," Bailey said.
The South Africans made an impact with the ball from the outset, destroying the Australian top order to have the home side in deep trouble at 34-4.