The 27-year-old carded a final round 66 for a 19-under-par 268 at the Royal Johannesburg and Kensington Golf Club.
Coetzee came from four shots down at the start of the final round to finish ahead of compatriot Justin Walters, Englishman Tyrrell Hatton and Jeong Jin of South Korea, who tied for second on 271.
Former Walker Cup star Andy Sullivan of England was fifth, one shot further back, after the best round of the day, a seven-under-par 65.
Coetzee's win came after 24 top-10 finishes on the European Tour.
"I'm ecstatic, I've been waiting a while and obviously there have (been) doubts creeping in but I've been trying to play it down," he said at the presentation ceremony.
Coetzee attacked the course from the opening hole on Sunday, birdying the first and fourth and two-putting the par five sixth for another birdie.
Soon after, overnight leaders Thomas Aiken and Walters both bogeyed the eighth to signal a dramatic change in the lead.
Coetzee stretched his lead to three shots on the back nine as he finished a faultless round with a total of six birdies.
Walters was two behind with two holes to play but failed to catch Coetzee, finishing with bogey to deny himself outright second place.
But along with Coetzee and Jeong, Walters won an invitation to The Open at Royal Lverpool in July by virtue of a top three finish.
(Reporting by Mark Gleeson; Editing by Josh Reich)
