The Swede, who carded a three-under 69, must win this weekend and hope Danny Willett finishes outside the top 10 to end 2016 as Europe's top golfer.
Nearest challenger Willett of England shot an opening-round 75, featuring a triple bogey on the second.
Stenson trails Felipe Aguilar, Jeunghun Wang and England's Ross Fisher by one.
"It would be nice to wrap up the Race to Dubai [this weekend], but I just want to play as well as I can for these two weeks and see where it takes me," said Stenson, referring to next week's season-ending DP World Tour Championship in Dubai.
"You're always going to look a little bit and see what the other guys are doing.
"I've got to focus on my game and I managed to do that, so I'm happy with today's work."
Stenson fought windy conditions in Sun City earlier in his round, but birdied holes 15, 16 and 17 to finish the day at three under par.
He was one of just 20 players in the field of 72 to finish below par and one of seven lying one shot off the leaders - a group that also included England's Chris Wood and Scotland's Richie Ramsay.
