Stenson had six birdies and three bogeys in a 69 for a 16-under total of 200. Coetzee and Magnus Carlsson were three shots back.
Stenson is looking for his first title since the Players Championship in 2009. He'll need to hold off a fast-finishing Coetzee on Sunday.
The South African had nine birdies and an eagle to break the course record at Serengeti. He had two bogeys on the back nine.
Martin Kaymer's 68 put him at 8 under, while Charl Schwartzel had a 74 to slip 10 shots off the pace.