Swede Stenson battled windy conditions earlier in his round but birdied 15 through 17 to leave himself one shot behind Chile's Felipe Aguilar, Englishman Ross Fisher and Jeunghun Wang from South Korea, who share the overnight lead at four under-par.
Victory at the $7 million (5.60 million pound) Nedbank Challenge, the penultimate event of the European Tour season, coupled with money-list rival Danny Willett finishing outside the top 10, would seal Stenson's place as the number one golfer in Europe in 2016.
That would also win him a bonus of $1.5 million ahead of next week's season-ending DP World Tour Championship in Dubai, contested by the tour's 60 leading money winners.
That looks a distinct possibility after Willett, who won at Sun City two years ago, carded a three over-par 75 that included a triple bogey on the par-five second hole.
Stenson is one of seven players a shot behind the front trio, a group that also includes England's Chris Wood and the home duo of Jaco van Zyl and George Coetzee.
The tough conditions made for some high scoring, with only 20 of the field of 72 finishing below par in their opening round.
"The wind out there makes Augusta look like a playground," Coetzee told reporters.
(Reporting by Nick Said; editing by John Stonestreet; nick.said@thomsonreuters.com; +27832722948; Reuters Messaging: Reuters Messaging: nick.said.thomsonreuters.com@reuters.net)
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