A closing 66 saw Homa finish on 19 under, four clear of Nicolai Højgaard.
The American began the final round with a one-shot lead at Gary Player Country Club and was briefly caught by Thorbjørn Olesen despite making birdies on four of his first six holes.
However, no sooner had he been joined at the top of the leaderboard than World Number Eight Homa fired a sensational approach over the water to 18 feet at the ninth and converted the eagle opportunity.
The eagle added to gains at the second, third, fifth and sixth – as well as a bogey at the fourth – saw Homa match Olesen’s front-nine 31 to lead by two on 18 under.
Olesen cranked up the pressure once more with a tap-in birdie on the tenth but, although Homa gave the chasing pack hope with a dropped shot on the 11th, the Dane carded consecutive bogeys at the 12th and 13th before a double-bogey at the 16th ended his challenge.
Homa birdied the 15th from seven feet and rattled in a 38-foot effort at the next to put the result beyond doubt.
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