Two-time major championship victor 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.
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.
"I was much better on the greens today than I had been the first couple days, so that was nice", said Jamieson. "I will be well aware of that tomorrow, so I've got to see if I can step up to the challenge".
Fleetwood would wrap up the Race to Dubai title with victory at Sun City, but the Englishman will also be focused on finishing strongly and extending his standings lead over Justin Rose ahead of the season-ending Tour Championship next weekend.
Major winners Martin Kaymer and Charl Schwartzel are also on the leaderboard at 2 under, with Kaymer, the 2012 champion in Sun City, moving up 31 places after his 69.
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 always play well here. Still an terrible long way to go but if I can obviously do what I did today, I'll be in with a good shout. It's a really tough course.
"There's a lot of history and a lot of great winners on the trophy and I'm very glad to be able to put my name on the trophy as well". You know, it's a course where you can't make more than bogey.
Italian Francesco Molinari signed for a 65 and the lowest round of the week to move to three under par alongside South African Haydn Porteous.
Friday proved a brutal test for most of the players, however, including Race to Dubai leader Tommmy Fleetwood, who dropped nine shots off the pace with a four-over-par 74. "Obviously it [winning] would be the biggest moment of my career". Download it today and continue to enjoy STV News wherever you are. "(It) just gets magnified towards the end of it".