Jamieson signed for a five-under 67 to move to eight-under par with overnight leader Frenchman Victor Dubuisson two-putting the last for a par in a round of 71 to be in second place on seven under par.
The duo of South Africa's Branden Grace (68) and Germany's double Major-winning Martin Kaymer (69) share third at five-under par.
Jamieson went into the third day of the $7.5 million event sharing fourth place and three shots adrift of Dubuisson but found himself tied for the lead courtesy of birdies at the second, fourth and ninth holes of the Gary Player-designed course.
The Glaswegian then went two shots clear with birdies at holes 13 and 14 before Dubuisson, playing two groups behind, birdied the 14th to cut the Scot's lead to just one.
"I was much better on the greens today than I had been the first couple days, so that was nice," said Jamieson.
"It's exciting now as I'm in a good position and tomorrow will be a new challenge, so looking forward to it."
In fact, Jamieson has contested 141 Tour events since his one and only victory in his very first event of the 2013 schedule and also in South Africa.
The Scot had shot rounds of 66 and 57 on a shortened and rain-affected Durban course to win in a play-off in what was the first of two Nelson Mandela Championships.
Dubuisson's round was a mix of four birdies and one fewer bogey as he kept alive a goal of a third Tour victory after his pair of Turkish Airlines Open wins in 2013 and 2015.
"I played as good as the first two rounds but my putting was maybe not as good," he said.
"I missed some good opportunities, but the problem is I felt like all day I had tricky, downhill putts, and I couldn't really go for it because I didn't want to. It's a really tough course.
"I kind of putted very easy. That's why I didn't make as many birdies as the day before."
Dual Ryder Cup star Francesco Molinari produced the lowest round of the day with the Italian managing seven birdies in his bogey-free 65 to share fifth place on three-under par.
And England's Tommy Fleetwood kept alive his goal of securing the Race to Dubai No 1 title by recording an eagle and five birdies in his score of 67 to move into a share of seventh spot at two-under.
"Today I was playing, trying to get myself into some kind of contention for the tournament," he said.
"I am mentally prepared for tomorrow, big time.
"Hopefully you've always got something to play for towards the end of the year, whether it's top 30, gets you in The Open or Top-10, Race to Dubai, and it's a new experience trying to win it.
"So, every shot counts and every shot should count throughout the year. (It) just gets magnified towards the end of it."
Last year, Sweden's Alex Noren came from a similar shot deficit to win "Africa's Major" and Fleetwood will need to do the same.
Leading third-round scores from the Nedbank Golf Challenge at Sun City, South Africa on Saturday (par 72, GBR/IRL unless stated):
208 - Scott Jamieson 68-73-67
209 - Victor Dubuisson (FRA) 68-70-71
211 - Branden Grace (RSA) 68-75-68, Martin Kaymer (GER) 73-69-69
213 - Haydn Porteous (RSA) 73-73-67, Francesco Molinari (ITA) 73-75-65
214 - Matthieu Pavon (FRA) 72-74-68, Tommy Fleetwood 73-74-67, David Drysdale 72-73-69, Louis Oosthuizen (RSA) 71-73-70, Charl Schwartzel (RSA) 69-73-72, Ross Fisher 70-71-73, Lee Westwood 70-70-74
215 -Richard Sterne (RSA) 74-72-69, Matthew Fitzpatrick 70-77-68, Hideto Tanihara (JPN) 69-76-70, Graeme Storm 69-75-71, Shane Lowry 72-71-72, Joost Luiten (NED) Richie Ramsay 73-70-72, Darren Fichardt (RSA) 71-69-75
216 - Ian Poulter 74-72-70, Alex Noren (SWE) 69-72-75
217 - Padraig Harrington 74-72-71