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Resuming on 102-3, captain Clarke and Warner plundered 108 runs in less than an hour before the latter was caught behind for 119 off the bowling of Morne Morkel in brilliant sunshine at Adelaide Oval.
Opener Warner's dismissal ended a breathless 155-run stand with Clarke that wrested control back to Australia after the pair had come together with the hosts reeling at 55-3 in the morning session.
In white-hot form following an unbeaten 259 in the drawn first test in Brisbane, Clarke went on to score his 21st test century and was on 104 at the interval, with Mike Hussey on 34.
Having steadied the Australian innings to lunch, Warner and Clarke stepped up the pressure as South Africa Graeme Smith rested paceman Dale Steyn and threw spinner Imran Tahir to the wolves.
With Jacques Kallis off the ground with a suspected hamstring injury and Vernon Philander a late withdrawal with a back strain, Tahir went for 68 runs off his eight overs, carted to all corners of the ground.
Resuming after lunch on 67, Warner needed only 14 balls to bring up his third test century, dispensing with the nervous 90s with just two deliveries.
The first saw Tahir lofted over his head for Warner's fourth six and the next despatched the spinner for four with a sublime cover drive to bring up his 100th run.
Having had his place in the test side questioned after an indifferent run of form, an ecstatic Warner bounded down the wicket and punched the air in delight as fans squeezed into the half of the ground not under renovation roared.
Warner had earlier welcomed all-rounder Faf du Plessis to test cricket by belting a first-ball full toss from the debutant for six into the scaffolding on the eastern side of the ground, one ball after another six in the same area off Tahir.
Clarke brought up his ton with a cut to the backward point boundary off Tahir, having survived an appeal for caught behind when on 73 off the bowling of paceman Rory Kleinveldt that umpire Billy Bowden gave not out.
South Africa referred the decision but it was turned down after a video review, the second declined for the innings, leaving the visitors with no more referrals.
The visitors had struggled from the outset after losing the toss and being asked to bowl, with pacemen Steyn and Morkel struggling for penetration.
But all rounder Kallis made an immediate impact when he came on by dismissing Ed Cowan for 10 with his third ball in the morning session, a searing yorker that struck the opener's toe before deflecting off the bat and looping back to the bowler for a simple catch.
In his second over, Kallis underlined his importance to his team by bowling Ricky Ponting for four when the former Australia captain's footwork fell apart to leave him slumped on the deck after the ball had clattered into his off-stump.
In the over between Kallis's strikes, a re-energised Morkel had Rob Quiney caught behind for a duck by Smith at first slip.
Kleinveldt, who went wicketless on debut in Brisbane, replaced Philander in the attack. Du Plessis makes his debut in the side in place of JP Duminy, while spinner Tahir was recalled after being benched at the Gabba.