The Australians hit back from their humiliating 32-23 defeat to the Samoans to hammer the injury-hit Springboks five tries to two in a dynamic attacking performance at the Sydney Olympic stadium.
Reinforced by seven big guns missing from last weekend’s humiliation, the Wallabies ripped apart the South Africans in a bonus-point demolition as they search for their first Tri-Nations trophy in a decade.
The Wallabies will also keep the Mandela Plate they won last year with their fourth win in five Tests against the Springboks.
South Africa left behind 21 injured front-line players for their Australasian leg of the Tri-Nations.
Sparked by halves Quade Cooper and Will Genia, the Wallabies were unrecognisable from their sloppy performance against Samoa and were always in command against the world champions.
The Springboks have yet to win in five encounters at the Sydney Olympic stadium and have only won four of their last 23 internationals in Australia.
The committed Wallabies showed they meant business from the outset and were 12-0 ahead after two tries in the opening 10 minutes.
Mercurial flyhalf Cooper broke the line to link with Kurtley Beale and James O’Connor, and off the next ruck the ball was quickly moved to the opposite wing where skipper Rocky Elsom got outside his man to send Alexander charging over.
O’Connor converted and Australia crossed the line again two minutes later when scrumhalf Genia made a break from inside his own quarter and sent flying winger Digby Ioane racing downfield.
Ioane stepped inside Springbok fullback Gio Aplon to score a try in his first Tri-Nations Test with the Wallabies on fire in the opening stages.
Flyhalf Morne Steyn reduced the deficit with a 30th-minute penalty but O’Connor restored the 12-point advantage with a penalty off a South African scrum infringement.
Steyn kicked his second penalty to have the Springboks trailing 15-6 at halftime.
Three minutes after the resumption South Africa’s centres Wynand Olivier and Juan de Jongh held off Cooper allowing the unpredictable Wallaby playmaker to spear through a gap for winger O’Connor to score a scrambling try.
O’Connor’s conversion lifted the Wallabies to a 22-6 lead.
The Wallabies grabbed their bonus-point fourth try and a 29-6 lead five minutes later when hooker Stephen Moore charged over off a Genia pass.
O’Connor kicked Australia further in front with a penalty and the points kept flowing when outside-centre Adam Ashley-Cooper scored after a cheeky tap-on from Cooper.
The Springboks claimed their first try in the 59th minute through replacement prop Chiliboy Ralepelle but they were well out of it at 39-13.
South Africa got a second try through skipper John Smit four minutes from full time.
The Springboks head to New Zealand to play the All Blacks in the second Tri-Nations match in Wellington next weekend.