Australia captain Pat Cummins spearheaded a pace barrage that tore through the Proteas before his side chased down a target of 34 to claim a win inside two days on a hostile Gabba pitch despite the best efforts of Kagiso Rabada, who took four quick wickets.
After finishing their first innings 66 runs in front midway through the first session Sunday, Australia dismissed the visitors for just 99 despite a fighting 36 not out from Khaya Zondo.
But the Australians then lost four cheap wickets in the chase as paceman Rabada ran amok, with Usman Khawaja, David Warner, Steve Smith and Travis Head all falling to catches behind the wicket.
However, Marnus Labuschagne and Cameron Green - aided by 15 extras - guided Australia home to give them a 1-0 lead in the three-match series on a day when 19 wickets fell.
SCORECARD | Australia v Proteas - 1st Test
"Tricky wicket. I thought the way Head and Smith batted (in the first innings) got us to this winning position," said Australia captain Pat Cummins.
Man of the match Head added: "Very difficult wicket, plenty for the bowlers. We saw that the whole game. Nice to be able to contribute and get a win."
Despite the victory, Australian selectors will be concerned with Warner's form after yet another failure.
Warner is due to play his 100th Test in Melbourne on Boxing Day without scoring a century in almost three years, as calls for him to be dropped grow louder.
The two teams went into the series both boasting high-quality bowling attacks, but Australia's batting always looked stronger.
And on a green Gabba wicket, South Africa's frailties at the top of the order were brutally exposed.
"Another 60 runs and we would have been in the game. Pretty spicy wicket, bowlers were licking their lips," said South Africa skipper Dean Elgar.
"I don't think we could prepare any better. Conditions weren't in favour for the batters."
South Africa slumped to 27-4 in the first innings and 5-3 in the second, positions from which they never recovered.
While the Australians also struggled at times, Head's superb 92 from 96 balls proved the difference between the two teams.
Australia started the day at 145-7 and South Africa did well to restrict them to 218, a lead of 66.
But the South African batsmen never looked up to the task of setting Australia a competitive total after slumping to 3-2 at lunch.
Stop the rot
Although Temba Bavuma and Zondo tried to launch a recovery in the middle session, they continued to lose wickets in clumps to a rampant Australian bowling attack.
Cummins, who finished with 5-42, started the second innings rot when he trapped his South African counterpart Dean Elgar lbw for two in just the second over.
Mitchell Starc then took the 300th wicket of his career when he bowled Rassie van der Dussen for a duck.
South Africa limped to lunch but Cummins struck again soon after the resumption when Sarel Erwee got a top edge to gully where the two-metre-tall Green leapt high to pull in a superb catch.
With South Africa staggering at 5-3, Bavuma and Zondo survived a torrid examination from Cummins, Starc and Scott Boland before slowly starting to chip away at the deficit.
Bavuma reached 29 before playing back to off-spinner Nathan Lyon to leave South Africa 47-4.
Boland then had first innings top-scorer Kyle Verreynne caught at second slip before bowling Maro Jansen two balls later to leave South Africa 48-6, still 18 runs from making Australia bat again.
Keshav Maharaj hit out to make a quickfire 16 before edging Starc to be caught behind, before Zondo and Rabada survived to the tea break.
But wickets fell quickly after the break with Cummins particularly dangerous with his impeccable line and length.