"It's a dream come true to win at Sun City and to win Africa's major", he said at the trophy presentation.
"It's exciting now as I'm in a good position and tomorrow will be a new challenge, so looking forward to it". With everyone expecting Jamieson to battle it out with France's Victor Dubuisson for the title, Grace snuck in with a bogey free round to become the first home winner since Trevor Immelman in 2007.
South Africa's Haydn Porteous posted a five-under 67 to be at three-under, while Race to Dubai leader Tommy Fleetwood hit back after a hard first two days to also post a 67.
His start apart, Grace believes the course suits him and hopes that his determination and comfort in the conditions will stand him in good stead.
Wiesberger made his move on the back nine with three straight birdies on Nos.
Branden Grace beat Luke Donald and Russell Knox...
"I'll take that for sure", said the 33-year-old whose only win on the European Tour came in 2013 at the now-defunct Nelson Mandela Championship at Royal Durban on the east coast. I try to play to the middle of the green.
They all had a share of the lead with four holes to play, but a brilliant 40-foot birdie putt on the 16th moved Grace to 11 under and with a one-shot victory over Jamieson.
And Grace would love nothing more. "I know now I can do it again".
China's Li Haotong finished fourth after making eight birdies in a blemish-free round of 64 - the lowest of the week - for a score of seven-under par.
Offaly's Shane Lowry remains one under par at the Nedbank Golf Challenge in South Africa after an underwhelming third round on Saturday morning.
"I was much better on the greens today than I had been the first couple days, so that was nice", said Jamieson.
The news was extra special for the strong South African after the news he received earlier in the tournament.
Louis Oosthuizen finished tied-eighth, after a final round 70 for a four-under score, while Haydn Porteous and Charl Schwartzel were tied-12th, two-under-par, after shooting 73 and 72 respectively.
He shot a final-round 68, which included five birdies and a bogey to be at five-under overall and a tied-sixth finish.