Furyk, who chipped in to win a four-way playoff last year, stands at 14-under-par 202 for a three-shot lead over Padraig Harrington.
The world's second-ranked player, Furyk has assembled three consecutive bogey-free rounds at the Gary Player Country Club. All three have been 68 or better.
On Saturday he collected birdies at Nos. 7, 9 and 11 -- where he also made birdies Friday -- and at the par-3 12th, where he hadn't made birdie in either of the first two rounds.
Furyk's birdies on the back nine were especially crucial, coming after Harrington had closed within a stroke.
Accuracy has been the name of the game for Furyk, who leads the 12-player field in greens in regulation and is second in driving accuracy. He is the only player in the field without a bogey.
Harrington fired a 7-under 65 and climbed from fifth place overnight into the position held by Henrik Stenson after Friday's round -- second place, three shots behind.
It was the lowest round of the tournament thus far and put Harrington at 11-under 205.
Stenson had a second consecutive 71 and dropped into a tie for third place with Ernie Els at 7-under 209. Els, a three-time winner and the tournament's all-time money leader, posted a 2-under 70.
Charl Schwartzel shot a 71 and stands fifth at 6-under 210, while Retief Goosen also had a 71 and is at 5-under 211. Trevor Immelman (73) and Jose Maria Olazabal (69) are two shots further back at 213.
Chris DiMarco made a nice move Saturday with a 6-under 66 that placed him in a tie for ninth with David Howell (73) at 1-under 215.
Sergio Garcia shot a 4-under 68, his first round under par, and moved to even-par 216.
Colin Montgomerie had his best round of the tournament by far with a 2-under 70, beating Friday's round by seven shots and trimming his score to 6-over par.
The players are competing for a lucrative offseason purse, which includes a first-place prize of $1.2 million.