Swedish pair Alexander Noren (65) and Fredrik Andersson Hed (66) were a shot adrift on 201.
Grace made six birdies, but was not surprised to run up a double-bogey six at Carnoustie’s fearsome 15th hole.
“I didn’t play particularly well, but I got it round,” he said. “But this course does that to you mentally.”
“You expect to hit a couple of bad shots out there but I kept fighting. Everybody calls it ‘Carnasty’ and that name for me says it all — for me it’s a lot tougher than the rest,” Grace added.
Having beaten fellow South Africans and multi major-winners Ernie Els and Retief Goosen in a playoff to land the Volvo Champions title in his homeland in January, Grace is not worried about leading from the front in the last round.
“I think if I keep hitting the ball the way I am and make the putts, anything is possible,” he said.
British Open winner Els, who gave Grace a place in his golf foundation when he was a teenager, showered praise on the leader who has also won this year’s Joburg Open and China Open.
“Branden has always been a quality player, but he has really come on now,” Els said. “Fortunately for him he hits it nice and low and it runs for ever. He could well even win an Open championship, he’s that good.”