The 21-year-old South Korean's eight-under-par round included an eagle and six birdies on the Gary Player course.
Home favourite Louis Oosthuizen is second on eight under after dropping two shots on the last two holes.
England's Andy Sullivan shot a 68 to move third on seven under, while overnight leader Alex Noren's 75 left him six off the lead.
Race to Dubai leader Henrik Stenson, who must win this weekend and hope Danny Willett finishes outside the top 10 to end 2016 as Europe's top golfer, is seven shots behind Wang after a 69.
Willett has struggled in what is the Race to Dubai's penultimate tournament but showed signs of improvement with a 67, which left him on par.
Find out how to get into golf with our special guide.
But it was Wang's third round which was the highlight of a day played in difficult conditions, when only 17 of the remaining field of 70 posted below-par scores.
"I'm so happy that I shot 64 and I'm more happy that I didn't have any bogeys," Wang told the European Tour website.
"I shot eight under on this course in this wind, I still cannot believe it.
"I don't want to think about any win. I just want to focus on the last 18 holes. I'll just try to do the same as today."
We've launched a new BBC Sport newsletter, bringing all the best stories, features and video right to your inbox. You can sign up here.
Jeunghun Wang shot a third-round 64 to move into a three-shot lead at the Nedbank Golf Challenge in South Africa.