Centre Elton Flatley finished with 19 points after landing all seven attempts at goal, including conversions of tries to his midfield partner Mat Rogers and flanker Phil Waugh.
But the Wallabies' relief at ending their three-match losing streak was tempered by a possibly serious injury to forward enforcer Toutai Kefu.
The Queenslander was taken from the field on a stretcher in the 79th minute after he was hurt in a tackle by Springbok prop Robbie Kempson while throwing the final pass for Waugh's try.
Kefu was taken to hospital after complaining of numbness in his legs following the blow to his neck.
His exit was worrying for the Wallabies because the powerful No.8 is a key figure in Australia's hopes of retaining the World Cup in October and November.
The Wallabies entered the match under enormous pressure but they found a spirited Springbok team which defended well despite having two front-rowers sent to the sin bin in each half.
High-flying New Zealand, which poured 50 points on both South Africa and Australia in their most recent matches, wouldn't have been shaking as they prepared to host their Tri-Nations rivals in the next two weekends.
But Australian captain George Gregan, who wore most of the criticism following
"It was a massive effort. We spoke about being patient and working harder and it would pay off for us," Gregan said.
Springbok captain Corne Krige lamented his team's ill-discipline after hooker Danie Coetzee was marched in the 39th minute for a professional foul and Kempson followed in the 67th minute for tripping but the Wallabies were unable to capitalise.
The Wallabies and Springboks showed their intention to spread the ball from the opening minutes but often lacked the execution to match the enthusiasm.
The Springboks had their best chance of scoring midway through the first half during an excellent attacking raid, which ended with five-eighth Louis Koen slotting one of his three penalty goals.
Rogers broke a 6-all deadlock in the first minute of the second half when he swooped on a loose pass from Koen to score beneath the posts.
The Wallabies were otherwise unable to break the defensive line until spreading the ball for man-of-the-match Waugh to dive over against the tiring Springboks.
AUSTRALIA 29 (Mat Rogers, Phil Waugh tries, Elton Flatley 5 pens, 2 cons)
SOUTH AFRICA 9 (Louis Koen 3 pens) at Suncorp Stadium. Referee: Paddy O'Brien (NZ).