The Californian carded 66 for a 19-under-par total of 269, ahead of Ryder Cup rival Nicolai Hojgaard, who finished on 273.
Hojgaard’s Danish compatriot Thorbjorn Olesen, who had launched an early charge but slumped in the final holes at the Gary Player Country Club, finished third on 274.
Homa, playing in his first tournament since the Ryder Cup in Rome last month, had a one-shot advantage at the start of the final round at the casino resort, some 200km northwest of Johannesburg, but was caught by Olesen who went on the charge with six birdies in an outward 31.
“It was a crazy day because I got off to such a good start but Thorbjorn was playing unbelievably and kept pushing us along,” said the winner.
An eagle on the ninth hole allowed Homa to retake the lead and he then had a lucky break on the 14th when a wayward shot hit an official’s buggy and landed back in play.
Birdies on the next two holes, including a 38-foot putt on the 16th, stretched his lead to three.
“It was an awkward putt," he said. "My speed on the greens was great for the first three days but... I don’t know if it was nerves... today it was just awful.
"That putt wasn’t very good either but fortunately it hit the back of the cup.”
Olesen’s double bogey on 17 increased Homa’s lead and ended the contest, with Hojgaard slipping into second place.
American Justin Thomas finished fourth, seven shots behind the winner after Englishman Dan Bradbury missed a putt on the final hole and slipped to fifth in the penultimate tournament on this year’s DP World Tour, whose championship in Dubai next week concludes the season.
