The 39-year-old had a strong opening nine holes on Thursday but faltered coming home. It was the reverse on Friday.
He turned at level par after three bogeys in a row between the sixth and eighth holes left him two shots behind Van Zyl, but five birdies on the back nine gave Stenson the advantage going into the weekend.
"I'm surprised given that on Wednesday afternoon I didn't think I would be able to tee it up," Stenson, who has been suffering with flu, told reporters.
"I thought I was done and dusted, so to be leading after two days, it's a turnaround to say the least. But the saying is 'beware of the injured or sick golfer' and I guess that's true."
Van Zyl's 68 included an eagle and two birdies but he battled with the pace of the greens and left several putts short.
American Robert Streb was denied a share of the lead when bogeys at the 16th and 17th cost him in a round of 66.
Australian Marc Leishman, who holed five birdies in his round of 68, was a further shot back.
England's Lee Westwood, a former world number one and twice winner of the tournament, dropped well out of contention with a nine-over 81, including a triple-bogey, double-bogey and six further dropped shots.
(Reporting by Nick Said in Cape Town, editing by Ed Osmond and Martyn Herman; nick.said@thomsonreuters.com; +27832722948; Reuters Messaging: Reuters Messaging: nick.said.thomsonreuters.com@reuters.net)
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