South Africa leave Australia with record chase
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It was Amla's 18th Test century and he faced 221 balls, hitting 21 boundaries.
After resuming at 99 not out on the third day, Amla took just three balls to reach triple figures, having faced a mere 87 balls.
At one stage, retiring Australian batsman Ricky Ponting was even given a bowl as Amla and de Villiers took the game away from the Australians.
De Villiers reached his 14th Test century in memorable fashion just before tea, audaciously reverse-sweeping spinner Nathan Lyon for three successive boundaries to reach the milestone.
He eventually fell for 169 as he appeared to tire, caught behind from the bowling of Mitchell Starc, having faced 184 balls, hitting 21 fours and three sixes.
South African Dean Elgar completed a nightmare Test debut, being trapped lbw by Johnson for a four-ball duck to complete a pair for the match.
Left-armer Starc cleaned up the South African tail to claim his first five-wicket haul in Test cricket and finish with six for 154 from 28.5 overs.