American Homa is on debut in South Africa but has mastered a difficult course and dropped just a single shot in 54 holes to finish his third round on 13 under-par for the tournament.
He leads France’s Matthieu Pavon by a single stroke after they had shared the top of the leaderboard overnight.
The Danish duo of Nicolai Hojgaard and Thorbjorn Olesen, who both shot 69, are two shots behind Homa and well in contention, while England’s Dan Bradbury (71) is a further shot back.
Pavon (70) carded five birdies and a bogey in his first 14 holes, but back-to-back dropped shots on 15 and 16 allowed Homa to leapfrog him on the leaderboard.
The American's only dropped shot in three days came on the par three fourth, and his consistency in hitting fairways and solid form with the putter were a feature of his play.
He managed a first eagle on the par five 10th hole to offset his earlier blemish as the six-time winner on the PGA Tour seeks a first victory on the European circuit, which includes a number of events in Africa.
England's Tommy Fleetwood, who has won the last two Nedbank Golf Challenge tournaments, could only manage a 71 on Saturday for a total of seven-under-par, six shots off Homa.
