The Austrian was part of a seven-strong group at the top of the leaderboard heading into the closing stages of day one at Gary Player Country Club, but an approach to four feet on the last hole saw him break out of the pack and get to 5 under.
Englishman Graeme Storm -- already a winner in South Africa this season -- was then in a group at 3 under that also contained 2011 Masters winner Charl Schwartzel, defending champion Alex Noren and Japan's Hideto Tanihara.
Wiesberger made the turn in level par, but three birdies in a row from the 10th catapulted him up the leaderboard. He bogeyed the 13th but picked the shot straight back up before chipping in at the 16th and making his closing gain.
"It wasn't easy to be honest," he told Sky Sports Golf. "It was quite breezy, quite steady directionwise, but still, the course is quite tricky off the tees. You want to get a lot of fairways to be able to attack the flags, and that's quite challenging when there's gusty winds.
"But I played all right. I've not had great success when I was here last time, but I approached it with a neutral mind, and I played a lot better than I have the last couple of weeks and putted good. I took a couple of chances, so that was nice, to get out there kind of relaxed and just let it happen."
Tommy Fleetwood will secure the Race to Dubai title with a win this week, but he stumbled to an opening 73.