Australia has won the third Test against South Africa by seven wickets after a disciplined bowling effort and brisk chase in Adelaide.

In an age of renewal for Australia's Test side under captain Steve Smith, the result was the perfect tonic after two sorry losses in Perth and Hobart, with a team featuring three debutants showing improved spirit and application to pull one back in the series.

The Proteas, who have been exceptional on the field for most of the tour, took the three-Test series 2-1 to continue their winning run of series victories on Australian soil that stretches back to 2008.

More importantly for Australia, the win ends a run of five consecutive Test losses, following a 3-0 away whitewash against Sri Lanka and the two earlier losses to South Africa.

"We bowled well and batted well in the first innings. We hadn't done that in the last two Tests," first innings centurion and man-of-the-match Usman Khawaja told Grandstand.

"First innings runs are worth double second innings runs most times, you pretty much always set up a win in the first innings.

"I think we did that well this Test match, and in the Test matches last year that we did do well and win, we did that too."

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The hosts dismissed the Proteas in Adelaide for 250, with opener Stephen Cook the last man out for a fighting 104.

Cook's innings potentially extended the 33-year-old's Test career after a series of struggle, but his partners had fallen cheaply on day three and the rot continued on Sunday when Quinton de Kock departed for 5.

De Kock's wicket signalled the end of South Africa's hopes when he missed a simple, straight delivery from Jackson Bird (1-54) that trapped him plumb in front.

Kagiso Rabada edged Josh Hazlewood (2-41) to the keeper for 7, before centurion Cook was bowled by Mitchell Starc (4-80) to wrap up the innings.

With David Warner returned to opening bat, he set about chasing down the runs in typically quick fashion, but he fell for 47 after a horrendous mix-up between the wickets with Matt Renshaw.

Mitchell Starc finished with figures of 4-80 as Australia quickly wrapped up South Africa's second innings. ( AAP: Dave Hunt )

Australia's tally of 1-64 quickly became 2-64 when Khawaja was dismissed LBW on review by Tabraiz Shamsi.

Steve Smith (40) and Matt Renshaw (34 not out) almost guided the hosts home — first conservatively, then briskly — only for Smith to edge Kyle Abbott to the keeper with two runs still to get.

Peter Handscomb joined Renshaw in the middle before Handscomb hit the winning run to secure a consolation win.

"It's always nice to win a game. We'll look back at it and obviously dissect it a little bit, and see what we did well and where we could do better," Khawaja said.

"But coming up against new opposition in Pakistan, they'll have different bowlers, we'll have different tactics, and we'll play on different grounds.

"We've got to figure out a way to do well in that series and do what we've done here for the remaining three games we have."

South Africa's Vernon Philander picked up the man-of-the-series gong for his 12 wickets, averaging 23.58.

Philander said the controversy surrounding captain Faf du Plessis over ball-tampering was not the reason South Africa came off second-best in Adelaide.

"I wouldn't say it put us off. It did distract us a little bit in our preparation leading up to this one, but I think it's part of the game and you're always going to find media flirting with one or two things," he told Grandstand.

"But I think [Australia] played the better cricket in this one and deserved to win it."

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