The 24-year-old carded a five-under 67 at St Andrews, one of three courses being used at the $5 million pro-am event, to finish with a 17-under total of 127.
Swede Joel Sjoholm (67) and Dane Thorbjorn Olesen (69) shared second place on 132, one ahead of South African Anton Haig (68).
Grace recorded his maiden victory on the European Tour at the Joburg Open in January and followed up by winning the Volvo Golf Champions that also took place in his homeland.
Last week he returned to his roots on the Sunshine Tour to triumph at the Vodacom Origins of Golf event.
"That was really good for me," Grace said after picking up six birdies including a sizzling run of five in six holes from the fifth.
"To have a good week like that put some fire in my game coming here to Scotland."
On Thursday, Grace equalled the lowest round on the European Tour when he fired a 60 at Kingsbarns.
"I didn't know quite what to expect today but I did get the round going with that birdie at the fifth where I hit a great rescue club to a foot," he said. "That settled my nerves.
"I think it helped I was playing a different course. If I had played Kingsbarns again after shooting the lights out yesterday I might have pushed it too much."
Sjoholm had an eventful time on the 18th at St Andrews where he pulled his tee shot so badly that it flew all the way across the adjoining first fairway and came within inches of going out of bounds.
The Swede then made the most of his good fortune by rolling in a 20-foot birdie putt up on the green.
The strangest incident of the day involved former world number three Paul Casey who had his ball stolen by a dog while lining up an eagle putt.
On the green at Kingsbarns's par-five 12th in two strokes, the Englishman looked on as the animal ran into the rough with his ball.
Casey, playing alongside Olympic swimming great Michael Phelps, went on to birdie the hole after the delay.
"It is the weirdest thing I have ever had happen on a golf course," said Casey after shooting a 69 for 141.
"I noticed the dog on the 12th tee and he followed us down the fairway before taking a real liking to my golf ball."
World number 118 Casey fell outside the top 100 in August for the first time in more than nine years owing to an injury-plagued 2012.
Martin Kaymer (71), who holed the putt that ensured Europe retained the Ryder Cup in Chicago last Sunday, was well down the field on 141.
Team mates Peter Hanson (70) and Paul Lawrie (70) were on 142 and 145 respectively.
British Open champion Ernie Els returned a 70 for 143.