Australia 30 (17)
Tries: Mitchell, Genia Con: O'Connor Pens: Giteau (5), O'Connor
South Africa 13 (3)
Tries: Fourie, Steenkamp Pen: Steyn
Springboks Schalk Burger (l) and Gurthro Steenkamp tackle Wallabies David Pocock
Australia condemned an ill-disciplined South Africa to their third successive loss to this year's Tri-Nations.
Matt Giteau kicked four of his five penalties before a Drew Mitchell try before half-time put the hosts 17-3 up.
The Springboks, who had Jaque Fourie and BJ Botha sin-binned, mounted a final-quarter fightback with tries from Fourie and Gurthro Steenkamp.
But the Wallabies held their nerve and a late try from Will Genia put the seal on a solid opening to their campaign.
They move on to face unbeaten New Zealand in the first of this year's Bledisloe Cup fixtures in Melbourne next Saturday.
The Springboks, meanwhile, return home with no points from their three away matches, with next to no hope of defending their title after suffering a third straight defeat for the first time since 2007.
We have to make sure we keep our full team on the park for the 80 minutes
"It is not a good start from us at all," acknowledged captain John Smit, whose side now have a four-week break before taking on New Zealand in Johannesburg on 21 August.
"We had to try to get some points away from home and we haven't so we have a lot of work to do back home to get some pride back.
"We have to make sure we keep our full team on the park for the 80 minutes."
Poor discipline had resulted in the world champions being reduced to 14 in their previous two Tests against New Zealand, and in Brisbane they saw yellow as early as the third minute when centre Fourie was sin-binned for a dangerous tackle on number eight Richard Brown.
It seemed as if the visitors would survive not conceding in the 10 minutes that Fourie was off, but with the centre about to return to action the Springboks were penalised at ruck and Giteau landed the penalty from 45m.
But within a couple of minutes South Africa were awarded their own penalty which Steyn, who averages 12 points a Test, fired over from about 40m.
South Africa coach Peter de Villiers suggested this week that referees may have favoured next year's World Cup hosts New Zealand in his side's last two Test defeats.
But against Australia, his side once again lost their composure.
First winger Bryan Habana was caught offside to allow Giteau to land a second penalty from near the right touchline to give the Wallabies a 6-3 lead, before the Brumbies player took his tally to 12 with two more efforts.
Until then South Africa had gone closest to scoring a try when Australia flanker David Pocock produced a brilliant tackle to bring down Habana 5m from the line.
That is the style we want to play all the time but it is not as easy as it seems
Wallabies captain Rocky Elsom
But a minute from the break, Rocky Elsom stole ball at a Springboks line-out and stormed into the Boks' 22. The ball eventually found it's way to Giteau, who popped up a pass to Drew Mitchell, who juggled the ball several times before touching down.
With Australia 17-3 ahead, the Springboks knew they had to come out and score early in order for the momentum to swing their way, but open-side flanker Ryan Kankowski played the ball off his feet.
Giteau, who missed the earlier conversion, made it five out of five penalties.
Worse was to follow when Botha was shown yellow for slowing down the ball in the tackle. Giteau was on target again to extend his side's lead to 23-3.
The numbers were then evened up when Wallabies centre Quade Cooper was sin-binned for a dangerous tackle on Steyn.
With Botha back on, the Springboks made the most of their man advantage when Ruan Pienaar elected to tap and go, finding skipper John Smit who in turn found Fourie, who pirouetted out of two tackles to force his way over.
With less than 10 minutes remaining, the Springboks went over again after they drove from a Victor Matfield line-out take, the huge figure of prop Steenkamp going over.
But the fightback was snuffed out five minutes from time by scrum-half Genia, who darted over from the base of a ruck to seal victory.
"It is great to have a win," said Wallabies skipper Rocky Elsom. "That is the style we want to play all the time but it is not as easy as it seems. It didn't go perfectly but we kept going and it paid off for us."
Australia: Ashley-Cooper, O'Connor, Horne, Giteau, Mitchell, Cooper, Genia, Robinson, Faingaa, Ma'afu, Mumm, Sharpe, Elsom, Pocock, Brown.
Replacements: Moore (for Faingaa, 55), Slipper (for Robinson, 58), Simmons, McCalman, Burgess, Barnes (for Giteau, 72), Beale
Sin-bin: Cooper (54)
South Africa: Kirchner, Aplon, Fourie, Olivier, Habana, Steyn, Pienaar; Steenkamp, Smit (captain), Botha, Rossouw, Matfield, Burger, Kankowski, Spies.
Replacements: Ralepelle (for Smit, 73), Van der Linde, Van der Merwe, Potgieter, Hougaard (for Pienaar, 73), James (for Steyn, 54), De Jongh (for Olivier, 54).
Sin-bin: Fourie (3), BJ Botha (46)