Grace closed with a bogey-free six-under-par 66 at Sun City to finish with an 11-under 277 total, pipping overnight leader Jamieson by a shot after he signed off with a 70.
The 33-year-old Scot got up and down from through the back of the green at the last to secure second place on his own, earning a career-best pay-day of around £630,000 in the process.
The brilliant effort catapulted him from 73rd to 23rd in the Race to Dubai, securing his spot in the season-ending DP World Tour Championship at Jumeirah Golf Estates in spectacular fashion.
Jamieson will be joined in that event by 29th-ranked Richie Ramsay and David Drysdale (54th), with Marc Warren agonisingly missing out by one spot after he slipped to 63rd following a disappointing finish in South Africa.
Stephen Gallacher’s season is also now over, but Jamieson has ignited his at an exciting time after producing four polished rounds on one of the toughest courses on the European Tour circuit.
The Glaswegian had just scraped into the penultimate Rolex Series event of the year and needed a top-15 finish to have any chance of moving on to the final one in Dubai. That he ended up doing so comfortably spoke volumes for his performance.
A shot ahead at the start of the final round, Jamieson had consolidated his position after picking up birdies at the second and sixth holes before having his first potential disaster of the week as a flyer out of a greenside bunker led to a double-bogey 6 at the eighth.
That allowed Dubuisson to get his nose in front before it became a three-way tie for the lead as the Frenchman was joined on 10-under by Jamieson and Grace as they both birdied the par-5 14th. Dubuisson then bogeyed the next, leaving the other two to effectively fight out over the closing three holes.
The decisive moment in that stretch came at the short 16th, where Grace rolled in a 30-foot birdie putt after Jamieson, who’d got lucky when his tee shot came back out of trees, saw his chip over a bunker from the rough lip out.
Sinking to his knees, he bit the blade of his wedge in frustration and then had salt rubbed into his wounds as Grace produced his moment of magic to effectively claim an eighth European Tour title triumph at the age of 29.