It was the first European Tour victory for Coetzee, who has a total of six wins across professional tours. It also was the fifth consecutive year and sixth time in the eight years of the Joburg Open that a South African won the event.
Coetzee was bogey free through Sunday's play and finished at 19-under 268 for the tournament.
Justin Walters, who was tied for the lead after Saturday's third round, was 1-over 73 in the final round and ended up tied for second at 16-under. Tyrell Hatton, with a final-round 66, and Jin Jeong, who shot 71 Sunday, were also at 16-under.
Thomas Aiken, who was tied with Walters going into the final round, had six bogeys in a 2-over 74 and tied for fifth.
It had been three years since Coetzee won the Sunshine Tour's Telkom PGA Championship but a strong showing Sunday ended the long spell between titles.
He had five birdies through the first 10 holes of the final round and held steady with seven parts and a 15th-hole birdie the rest of the way.