Westwood's three-round total, 14-under 202, gives him a chance to become a 19-time winner on the European Tour in Sunday's final round at the Pearl Valley Estates in Paarl, South Africa.
He quickly put pressure on overnight leader Michael Lorenzo-Vera of France with birdies at the first and third holes and his birdie at the par-five 18th led to his two-stroke cushion.
"You want to be leading, so I'm pleased with the position," said Westwood, the world's 10th-ranked player.
"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."
Lorenzo-Vera's third round included two double-bogeys and an eagle at the fifth, and his even-par 72 left him tied for second place at 12-under 204 with Northern Ireland's Gareth Maybin (69).