The Wallabies finally rediscovered their attacking edge to score 20 points in the second half and claw their way back to overpower the Springboks after trailing 13-6 at half-time.
With only one try in their two prior Bledisloe Cup defeats at the hands of New Zealand, the Wallabies looked in real danger of having their four-match winning streak against South Africa snapped with a listless first-half performance that must have made the under-pressure Deans anxious.
However, the unerring accuracy of Berrick Barnes, who was six-from-six with the boot but appeared to suffer a calf injury late in the match, combined with second-half tries to reserve Scott Higginbotham and prop Ben Alexander to give the Wallabies a welcome win.
Wallabies captain Will Genia also limped off with a knee injury late in the game.
Higginbotham had only been on the field for a couple of minutes when he broke a tackle and stormed over next to the posts in the 56th-minute to score the Wallabies' first try of the night and give the home side a one-point lead that became three when Barnes made the simple conversion for a 16-13 advantage.
Morne Steyn levelled the scores at 19-19 with a penalty in the 68th minute, but only 60-seconds later Alexander crossed in the corner to make it 24-19, after the try was confirmed by the video referee.
A superb conversion by Barnes gave the Wallabies a seven-point lead, but even as the ball sailed through the flyhalf was clutching at his calf and he left the field soon after.
It was to the be the last score of the game, a late surge for an equalising try by the Springboks ending with a penalty to Australia in the dying seconds.
It was a bitter pill for the Springboks, who were themselves coming off a disappointing 16-16 draw with Argentina and looked to have the game at their mercy at the break.
They scored the only try of the first half when winger Bryan Habana dived over in the 20th-minute, but never really threatened the Australian try line in the second half.
It was a nervous start for the Wallabies, despite winning plenty of possession, and they must have been relieved when they finally broke their recent scoring drought with a Barnes penalty in the 18th-minute.
They were held scoreless by the All Blacks in their previous outing, a 22-0 loss at Eden Park a fortnight earlier, and Barnes's easy conversion settled Australian nerves a little.
The Wallabies had a lot of the ball early, but couldn't turned it into much in the way of genuine scoring thrusts, their best chance going begging in the seventh minute, when they transferred the ball wide but Barnes couldn't hit Adam Ashley-Cooper with his pass.
The Springboks punished them when they got the ball shortly after the Barnes penalty and pressed the Australian line strongly.
Although the South Africans butchered a couple of golden opportunities to score the game's first try, Habana made up for it when he picked the ball up and dived over next to the posts for the 42nd-try of his Test career. – Sapa-AFP.