The Austrian's 67 took him to five under par, one shot ahead of a group of four players including Scott Jamieson and home favourite Branden Grace. Charl Schwartzel and defending champion Alex Noren are a shot further back.
Wiesberger, who is placed 12th in the Race to Dubai, reached the turn in level par after two birdies and two bogeys, but rattled off six birdies on the back nine, with a solitary bogey at the 11th.
"I made a lot more birdies than I have in recent weeks, when I have been struggling to get the ball in the hole," he said. "I don’t want to jinx it, but I felt like I found a little bit more on the putting green, a little bit of pace and some confidence.”
Tommy Fleetwood, who could wrap up the Race to Dubai this week with victory at Sun City, has some work to do after an opening 73 that leaves him one over par.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Fellow Englishman Lee Westwood was three shots off the pace after a two-under-par 70.
(Reporting by Nick Said; Editing by David Goodman)
