Oosthuizen carded a final round 68 for a 12-under-par total of 276, one stroke ahead of compatriot Branden Grace.
The 2010 Open champion looked to have blown his chances when he carded a bogey on the 16th to fall a shot behind Grace, but back-to-back birdies in the final two holes put him in front.
Overnight leader Tommy Fleetwood of England managed a par round of 72 on Sunday to finish two shots behind Oosthuizen and tied third with Joost Luiten from Netherlands.
(Reporting by Nick Said in Cape Town; Editing by Josh Reich)