Teenager Canan Moodie scored a try on debut as South Africa snapped a nine-year losing streak on Australian soil in a fiery Rugby Championship contest.
Centre Damian de Allende, flanker Franco Mostert and winger Makazole Mapimpi also crossed to help the world champions get back to winning ways after two straight defeats and gatecrash the opening party at the rebuilt Sydney Football Stadium.
Australia, having named an unchanged starting side for the first time in three years, suffered another rash of injuries but were inaccurate in their play all evening and slumped to a fourth defeat in seven matches this year.
"It was a tough week last week but I'm grateful for the way the boys stood up," said South Africa captain Siya Kolisi.
"People were hurting back home, it's been a long drought for us, 11 games without a win here."
Springboks coach Jacques Nienaber had rung the changes after last week's 25-17 loss to the Wallabies at Adelaide Oval and he got the response he wanted.
The visitors came out as if on a mission, hurtling into contact, kicking into space and mauling from every lineout to put immense pressure on the home side.
They got their reward in the ninth minute when lock Eben Etzebeth charged towards the posts and managed to get the ball away for De Allende to dive across the line.
Wallabies lock Matt Phillip was sent to the sin bin for an infringement during the preceding siege of the line but the home side survived another wave of attacks.
Out-half Noah Lolesio got Australia on the board with a penalty just after the half-hour mark but the Springboks got their second try just before the break.
Scrum-half Jaden Hendrikse sent up a huge box kick and 19-year-old winger Moodie leapt above Marika Koroibete to snatch the ball out of the air and race away to give the Springboks a 12-3 half-time lead.
South Africa kept up the intensity at the of the second half and again got early reward, Mostert barging across the line after quick ball had opened up space on the right wing.
By this stage, the Wallabies had lost inside centre Hunter Paisami and Lolesio to knocks, while prop Taniela Tupou was unable to come off the bench because of an injury.
They battled hard but the Springboks charged back to score a fourth try in the 71st minute through Mapimpi, who finished well in the left corner but was then sin-binned for over-enthusiastic celebrations in the face of Koroibete.
Mapimpi's action, revenge perhaps for Koroibete's try-saving tackle on him in Adelaide last week, sparked a huge melee that sucked in most of the players from both teams.
The last nine minutes were chaotic and replacement loose forward Pete Samu crossed for Australia's try after a sequence of play that saw a second South African, Willie le Roux, shown a yellow card for a deliberate knockdown.
"Another week of poor discipline and that probably the most disappointing thing," said Australia captain James Slipper.
"We didn't really fire a shot, they were just dropping bombs on us all night."
The bonus-point victory elevated the Springboks to second place in the standings behind reigning champions New Zealand, who beat Argentina 53-3 in Hamilton earlier on Saturday, with two rounds remaining.