Amla, Smith guide SA to 292-run lead in 3rd test
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Robin Peterson took the last three Australian wickets with his left-arm orthodox spin after Matthew Wade's rearguard 68 came to an end.
Australia only added two runs to its overnight total before opener David Warner (13) was caught behind, playing rashly outside off stump to Steyn to spark a half hour of carnage and a collapse of 4-11 – including the wickets of ex-captain Ricky Ponting (4) and skipper Michael Clarke (5).
Ponting got a standing ovation from the crowd when he went in to bat in his 168th and last test match and got off the mark quickly with a single, then watched as night watchman Nathan Lyon was out two balls later, slicing Steyn to du Plessis at gully.
Ponting faced seven balls before he was trapped lbw by Vernon Philander.
Australia's position deteriorated further when Clarke got an edge to a perfect away swinger from Steyn to make the total 45-6.
It was Clarke's first serious failure of the series, after scoring double centuries in the first innings of both the drawn first and second tests.
It could have been even worse for Australia.
Wade should have been out without scoring but Amla missed a run-out chance at the striker's end after Hussey took off for a dangerous, quick single.
But Wade recovered to share partnerships of 55 with Mike Hussey (12) and 40 with Hastings (32) to drag the hosts to 140-8.
Wade raced to his 50 from 51 balls, raising his half century with his third six, but dug in after the lunch break and slowly helped reduce the deficit before his dismissal triggered another late collapse.
Peterson bowled Johnson (7), also attempting to sweep a ball that didn't turn, and Hastings drove him to long-off.
The No 1 ranking is on the line in Perth, where South Africa needs only a draw to retain top spot and Australia requires a victory.