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They, however, lost the three-match series 1-2 after losing the first two Tests. It was Australia's first Test victory since beating New Zealand by seven wickets in Christchurch in February.
Australia chased down 127 runs for victory in the fourth innings after dismissing the Proteas for 250 on the fourth day of the pink-ball Test, according to www.icc-cricket.com.
Debutant Peter Handscomb (1 not out) hit the winning run with fellow newcomer Matthew Renshaw on 34 as Australia finished on 127 for 3. Handscomb came to the wicket after Steve Smith, the captain, was caught behind for 40 off Kyle Abbott with two runs to win.
The home side also lost the wickets of David Warner and Usman Khawaja during the chase. Warner blazed 47 off 51 balls before he was run out. Khawaja couldn't open his account in the second innings after cracking a century in the first.
South Africa, who conceded a 124-run first innings lead, were always under pressure to build a defendable target.
They lost the dangerous Quinton de Kock (5) early on the day. South Africa resumed on its overnight score of 194 for 6 but could only add 56 runs before it was dismissed for 250. Stephen Cook, the opener, delayed the end as much as he could with a defiant century (104).
Cook was the last man out when he was bowled by Mitchell Starc 45 minutes before the tea break.
Australia 383 & 127/3 (David Warner 47)
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