The 12th-ranked Swede dropped a shot at the par-3 seventh, but made five birdies on the first nine. He added three more birdies and an eagle on the last nine.
Rory Sabbatini (68) is second after birdies on the first, sixth, 10th and 11th holes. Lee Westwood (70) was the only other player to break par on a course where the rough was especially tough around the fringes of the greens.
Stenson tied the 2002 mark set by Ernie Els, who shot 63 in the final round en route to a victory.
It is a strong field and I just need to stick my head down and do my business for another three days, Stenson said. I guess 9 under is always going to put a bit of ground between the leader and the rest.
Stenson, who won the World Cup title with partner Robert Karlsson last week in China, said he was feeling tired coming into the Nedbank Challenge.
I just sort of carried on. We shot a 63 in the foursomes in the World Cup, and I started off with a 63, so I hope to keep it going for the rest of the week.
Sergio Garcia (72) picked up two birdies to counter his two bogeys, and only managed to make half of the greens. He was tied with defending champion Trevor Immelman, K.J. Choi, Karlsson, Luke Donald and South African Open champion James Kingston.
Justin Rose and Kenny Perry each shot 73, while Miguel Angel Jimenez was last in the 12-man field with a 75.