Chasing a first European Tour win since 2012, when he stormed to an impressive four titles, Grace established a commanding five-shot lead at the halfway stage after firing excellent round of 62 and 66.
Saturday 72 level-par from Grace meant Denmark's Lucas Bjerregaard closed to within one shot but his final round collapsed the chasing pack could not make a dent in the leader on Sunday.
Grace carded 68 to complete a 20-under tournament and finish seven shots clear of compatriot Louis Oosthuizen in second.
Andrew Johnson came in third on 11-under, one clear of Danny Willet and Trevor Fisher, who tied for fourth position.
A bogey on the opening hole saw Bjerregaard hand Grace an early lift and victory ambitions already appeared to be slipping away from the European when his playing partner birdied two.
But Bjerregaard got up and down for a birdie on six to close to within three, Grace having picked up another shot at four.
It proved a false dawn as Bjerregaard found water and returned a triple-bogey six on the next hole and his back nine unravelled in horrific fashion - the 23-year-old coming home in 50.
Oosthuizen, Johnson and Willet soon became Grace's most credible challengers but he kept them at a safe distance with timely birdies on 11, 13 and 15.
A bogey on 16 by the leader was placed into context as Willett dropped six shots over the final three holes and Oosthuizen played into the water on 18, with margin for error long since exhausted.
"It's been a phenomenal week," Grace told the European Tour’s official website after becoming the first player to win both the Alfred Dunhill Championship and its affiliated Links Championship.
The winner pinpointed greater poise off the tee with a new driver as being central to a consistent and triumphant display.
"It's been a long year, a hard, year but now it's a fairytale ending just before Christmas," he added.
"One of the main things this week has been the driving. I just put a new driver in the bag in Dubai and that’s been the key this week."