Westwood finished 54 holes at 14-under 202 and is two shots clear at Pearl Valley Estates.
Overnight leader Michael Lorenzo-Vera overcame two double-bogeys in the third round for an even-par 72. He managed an eagle at the fifth, but fell into a tie for second place with Gareth Maybin, who carded a 3-under 69 on Saturday, at minus-12.
Two-time U.S. Open champion Retief Goosen (69), George Coetzee (68) and Rory McIlroy (67) are knotted in fourth place at 11-under 205.
Westwood started strongly on Saturday with birdies at the first and third holes. Lorenzo-Vera birdied the second, but fell down the leaderboard thanks to a double-bogey at the par-5 third.
Lorenzo-Vera got back in front thanks to an eagle at the par-5 fifth hole. Both Lorenzo-Vera and Westwood parred the remaining holes on the front side, but Westwood moved ahead thanks to some miscues by Lorenzo-Vera.
The overnight leader bogeyed the 11th hole after a drive into the left rough, then double-bogeyed the par-3 12th when his tee shot went on the other side of a creek.
Westwood kept making pars and found himself one clear of McIlroy, who was in the clubhouse, and two in front of the struggling Lorenzo-Vera.
Both Lorenzo-Vera and Westwood birdied the par-4 14th and both made birdie at the par-5 closing hole. That allowed Westwood to keep his two-shot cushion.
'It's a good position to be in,' said Westwood. 'You want to be leading, so I'm pleased with the position. I'm just pleased with the way I played the last three days, I've been very solid and made just one bogey, I think.'
Westwood is an 18-time winner on the European Tour, although he has not visited the winner's circle since the 2007 British Masters. This is his 18th 54-hole lead on tour and he's only hoisted the trophy eight of the previous 17 times.
'I have to think and not get too ahead of myself,' admitted Westwood. 'All week long, all I've tried to do is minimize the mistakes and just get around. I'm just enjoying it and I look forward to going out and playing every day the way I'm hitting the ball. It's a golf course I enjoy playing.'
Damien McGrane (72) and Bernd Wiesberger (65) share seventh place at 10-under 206, while former Masters runner-up Len Mattiace (71) and Ross McGowan (71) are knotted in ninth at minus-9.
Ernie Els, a four-time winner of this championship, got off to a horrible start on Saturday with a triple-bogey at the first. Sadly for the three-time major winner, it was not his only triple-bogey of the round. Els tripled 11 and walked off with a 5-over 77.
Els fell into a tie for 37th place at 5-under 211.