The 32-year-old went into the final round with a one-shot lead but extended his advantage in formidable fashion as he shot 67 for a four-round total of 269 to claim the first prize of 1.25 million dollars.
It was the first European Tour success for Leishman, who produced a consistent performance off the tees and bagged four birdies on the back nine amid sweltering temperatures at the Sun City resort on Sunday.
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Stenson, who is due for knee surgery next week, had to extricate himself from several difficult lies but was always under pressure as he attempted to stay in touch with the sturdy Australian.
The 15th hole ended the contest as 39-year-old Stenson hit a bogey while Leishman sank a birdie to suddenly pull away to a five-shot lead.
Stenson finished 13 under after a final-round 72, including a three putt on the last hole.
Chris Wood of England finished third on nine under par after American Robert Streb double-bogeyed the last hole to slip from 10 to eight under, where he shared fourth place with defending champion Danny Willett, who overcame back problems on Friday, Frenchman Victor Dubuisson and leading home golfer Branden Grace.
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