Grace finished at 17-under-par, one shot ahead of former Augusta State golfer Jamie Elson, who catapulted himself into second place by shooting 63.
The 23-year-old Grace began the final round with a three-shot lead over compatriot George Coetzee and Richard Finch, of England.
Finch struggled to 78, three-putting three times on the front nine, to end nine shots off the pace.
Coetzee closed to within two shots of the lead with birdies on the fifth, sixth and eighth holes, but the burly South African faded on the back nine after a double-bogey on the par-4 13th when he hooked his approach shot into the water.
Coetzee, ranked 80th in the world, finished with 75 to tie for 14th place.
Grace, a former member of the Ernie Els Foundation in South Africa, put together nine consecutive pars on the back nine to hold off Elson and six golfers who finished in a tie for third on 14-under.
The pressure of leading seemed to affect Grace at the start of the final round as he bogeyed the par-3 second hole. But an approach shot to within eight feet on the par-4 ninth set up a birdie that seemed to settle the former South African amateur stroke play champion.
“I played superbly today, my approach shots were amazing. I stuck to my game plan and kept hitting good shot after good shot. I couldn’t dream of better approach shots than what I played on the last five holes,” Grace said.
Grace’s back nine was the epitome of solid golf under pressure as he made no mistakes off the tee and was superb with his irons. The margin of victory would have been greater if he had not narrowly missed a number of birdie putts.
“The opportunities were there, but I told myself first of all not to mess up and then to just keep giving myself chances. I struggled to get the lines exactly right, the greens were immaculate, but if you were a little bit off, you ended four feet away,” he said.
“Obviously it’s awesome to win, it’s been coming a long time and it’s really nice to have the first win back home.”