Tries from hooker Adriaan Strauss, fullback Zane Kirchner and wing Willie le Roux took South Africa tantalisingly close to the extra point while flyhalf Morne Steyn kicked two conversions and three penalties.
The victory took the home team to the top of the table although they have played a game more than New Zealand who meet Argentina later on Saturday.
South Africa had been hoping for a bonus-point victory in their bid to set up a potential title decider against the All Blacks on Oct. 5.
Australia's only try came from debutant winger Chris Feauai-Sautia with two minutes remaining. Christian Leali'ifano also landed a penalty that was the first score of the game.
"It's a great sign of this team that we beat Australia by 20 points but are not totally happy," coach Heyneke Meyer told a news conference.
"The whole week has been tough, all the talk of only a bonus-point win being good enough. After the game the players weren't happy but I thought we played some great rugby."
The match was a physical affair with French referee Jerome Garces showing four yellow cards.
South Africa pair Flip van der Merwe and Duane Vermeulen were sent to the sin-bin, as were Wallaby duo Michael Hooper and Sitaleki Timani.
The opening try for the Springboks came from some positive play inside the first 15 minutes as Steyn turned down a kickable penalty and opted instead to boot the ball into touch in the corner.
South Africa won the resulting lineout and drove close to the line, Strauss eventually barging over from close range.
They were in for another try just two minutes later, this one completely different in its construction as the home side exposed the Wallabies out wide.
After running the ball from just outside their own 22, Jean de Villiers missed out two team mates with his pass, allowing JJ Englebrecht to sprint clear.
With just fullback Israel Folau to beat, his inside ball to Kirchner saw the Springbok number 15 coast home.
Australia could not cope with the pace and power of the Boks, the shell-shocked Wallabies spared more blushes by some poor handling and passing from the hosts.
Wallaby flanker Hooper was the first to be sin-binned for a dangerous tackle on lock Eben Etzebeth before an unnecessary use of the elbow from lock Van der Merwe saw him receive a deserved yellow card.
The teams turned at the break with South Africa in total command and leading 23-3.
The Wallabies did not retreat to their dressing room at halftime, instead staying on the pitch and receiving a public dressing down from coach Ewen McKenzie.
It seemed to have the desired effect as Australia improved in the second half, though the result was never in question.
Vermeulen and Timani received yellow cards for deliberate knockdowns while Le Roux took South Africa to within sight of a bonus point with nine minutes to play.
Teenage debutant Feauai-Sautia then made it a day to remember for him as he collected a long crossfield kick from Quade Cooper to touch down.
"It was not a good night at all, we didn't do well early in the game and we played without the ball for half the game. We were better in the second half but we were chasing it by then," said McKenzie.
"We had opportunities to put pressure on them but lost out through poor execution. That's where we are at the moment, all we can do is keep plugging away."
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- Adriaan Strauss