The Scotsman won the weather-shortened Nelson Mandela Championship in the 2013 European Tour season, but taking home a check for just under £940,000 and a first Rolex Series trophy in Sun City, South Africa, would dwarf that achievement and boost his chances of making Thomas Bjorn's Ryder Cup team next year.
A bogey-free 67 moved Jamieson, 33, to eight under and holding a narrow advantage over France's Victor Dubuisson, who signed for a 71 after holding a two-shot overnight lead.
Jamieson was a picture of consistency as he made birdies on the second, fourth, ninth, 13th and 14th.
"It's exciting," Jamieson told the European Tour's official website. "I'm in a good position, Sunday will be a new challenge. Still an awful long way to go but if I can obviously do what I did today, I'll be in with a good shout.
"It would be the biggest moment of my career, I'll be well aware of that. I've got to see if I can step up to the challenge."
Two-time major championship winner Martin Kaymer was at five under alongside home favourite Branden Grace, with another South African in Haydn Porteous and Italian Francesco Molinari two shots further back.
Englishman Tommy Fleetwood would take the Race to Dubai title with a win on Sunday, but he was six shots off the lead after a third-round 67.