The Australians chased down 127 runs for victory after dismissing the tourists for 250 on the fourth day of the pink-ball Test.
The Australians, rejuvenated by five team changes in response to two humiliating defeats to the Proteas to lose the series, chased down 127 runs for victory after dismissing the tourists for 250 on the fourth day of the pink-ball Test.
Debutant Peter Handscomb hit the winning run to finish one not out with fellow newcomer Matthew Renshaw on 34 in Australia's 127 for three.
Handscomb came to the wicket after skipper Steve Smith was caught behind for 40 off Kyle Abbott with two runs to win.
"It's much better to be on this side of the fence," Smith said.
"A little bitter-sweet, it was a disappointing series, we were outplayed in the first two Tests.
"But I'm really proud how the team came back in this game, new players came in, they stood up and we showed some fight and character."
The home side also lost the wickets of David Warner and epic first-innings centurion Usman Khawaja on the way to victory.
Warner blazed 47 off 51 balls before he was run out in a mix-up and Khawaja, who batted for almost eight hours in the first innings, lasted just two balls before he was leg before wicket to a Tabraiz Shamsi wrong'un.
Australia's victory saw off the threat of South Africa taking an unprecedented series clean sweep Down Under and was just the tonic after recrimination over the team's abject form.
But after seizing a 124-run innings lead, Steve Smith's team broke down the Proteas resistance for their first Test victory since beating New Zealand by seven wickets in Christchurch in February.
Once the dangerous Quinton de Kock was removed for five early on the fourth day, South Africa were always under pressure to build a defendable target to bowl at the Australians.
Both teams wore black armbands to mark the second anniversary of the death of former Australia Test opener Phillip Hughes, who died from bleeding on the brain after being hit on the neck by a rising ball during a domestic match in Sydney.
South Africa held outside hopes of repeating their predecessors' famous five-run victory in Sydney 22 years ago when they bowled out Australia for 111.
"Very happy. Our mission was successful. The last four days was not planned, but we came here to win the series, fortunately for us it was in Hobart (second Test)," South Africa skipper Faf du Plessis said.
"It was an incredible series to beat Australia 2-1 and to do it three times in a row is a huge effort."
The Proteas, who thrashed Australia in the first two Tests to claim a third consecutive series Down Under, added 56 runs to their overnight lead before they were bowled out with opener Stephen Cook scoring a defiant century.
Cook raised his second Test century and first against Australia with a pull through square leg for four off Josh Hazlewood.
It was a positive finish to an underwhelming series for Cook, who had scores of 0, 12, 23 and 40 in his other innings before his timely ton off 235 balls.
Cook was the last man out when he was bowled by Mitchell Starc 45 minutes before the tea break.
De Kock, who mastered the Australian bowlers, especially spinner Lyon, in the first two Tests, went cheaply.
Australia sought a review after Jackson Bird's leg before wicket appeal was turned down and replays showed the ball hitting de Kock's front pad pitching on middle and leg stump.
It was a massive blow for the Proteas' hopes of giving Australia a challenging target to chase down in the fourth innings.
Philander, named man-of-the-series, was one of Starc's four victims when he was leg before wicket for 17, losing a review in the process.
Kagiso Rabada lasted just nine balls before he edged a leg-side delivery from Hazlewood to a diving Matthew Wade and Cook's dismissal ended the innings.
The second pink-ball Test played in Adelaide drew a total of almost 126,000 fans over the four days.