Grace grabbed the lead Thursday with a course-record 12-under 60 on the Kingsbarns course at St. Andrews and retained the advantage through rounds 2 and 3.
The South African wrapped up the triumph Sunday, reeling off three straight birdies on the back nine to hold off a charging Thorbjorn Olesen and end up with a two-shot margin of victory.
Oleson just missed an eagle on the 18th, settling instead for a final-round 68 to finish at 20-under.
Securing sole possession of third place at 18-under was Alexander Noren (69), while Joel Sjoholm (70) took fourth at minus-16.
Former Alfred Dunhill champ Stephen Gallacher (71) was part of a seven-way tie for fifth at 15-under.