The home side finished convincing winners after leading 23-3 at half-time, but scored only three tries and missed the bonus point they wanted to put pressure on title rivals New Zealand.
Hopes were high of a four-try victory when the Springboks scored two within 15 minutes of the kick-off, but they had to wait until the closing stages for the only other one.
South Africa did move to the top of the table on scoring differentials, but New Zealand have a chance to move five points clear when they play in Argentina late Saturday.
Australia were first on the scoreboard with centre Christian Leali'ifano kicking a simple penalty on seven minutes after No. 8 Duane Vermeulen was caught offside.
But the advantage was short lived as fly-half Morne Steyn, winning his 50th cap, slotted his first penalty of the match after captain James Horwill did not roll away at a maul.
Much greater happiness was to follow for the near capacity crowd as the Springboks scored two tries within three minutes to build a 17-3 lead with 16 minutes gone.
Hooker Adriaan Strauss dotted down after 13 minutes, driving over from close range after a skip pass from scrum-half Fourie du Preez, and Steyn converted.
Full-back Zane Kirchner claimed the second try, but it was a magnificent team effort that had its origins at a maul deep in green and-gold territory.
Du Preez set the move in motion, and a series of skip passes and a great run by centre JJ Engelbrecht breached the Australian defence before Kirchner ran in.
Another Steyn conversion followed by two penalties closed the scoring in an opening half marred by a yellow card to each team.
Wallaby flank Michael Hooper was first to be sin binned, walking to the touchline after 28 minutes for a dangerous tackle on lock Eben Etzebeth.
Hooper felt hard done by, and so did Springbok lock Flip van der Merwe after his 40th-minute card for leading with an elbow against Joe Tomane.
However, French referee Jerome Garces was fully justified in making both decisions after consulting with the television match official.
Bismarck du Plessis, wrongly red carded during a defeat in New Zealand two weeks ago, replaced Strauss to warm applause 10 minutes into the second half.
There was an equally loud welcome for local flank Siya Kolisi, when he entered the fray on the hour mark of a game crying out for some excitement.
Australia gained from the introduction of Will Genia for Nic White at scrum-half and were proving much more stubborn opponents than in the early exchanges.
South Africa were doing their share of defending and as the Test reached the final 10 minutes, a four-try bonus point seemed a distant dream.
It did not help the Springbok cause that Vermeulen became the third player to be yellow carded, paying the price for a deliberate knock-on.
But after 40 point-less minutes, South Africa scored a third try eight minutes from time with another superb Du Preez pass enabling right-wing Willie le Roux to squeeze in at the corner.
Steyn fell just short with his touchline conversion -- his first goal-kicking failure of the match -- but success was assured with a 25-point advantage.
Replacement forward Sitaleki Timani added to the misery of the visitors by getting a yellow card five minutes from time.
But the side that opened the scoring also closed it with substitute left-wing Chris Feauai-Sautia snatching a late unconverted try.