His winning total was 18-under 270, two strokes better than England's Justin Rose (69).
"Obviously I'm delighted to win, but more especially in the manner that I did," said Dougherty after his second European Tour victory. "I'm going to go cry a little."
He entered the week ranked 100th in the world.
Dougherty won the event despite starting the final round at St. Andrews with consecutive bogeys on the first two holes, but made four birdies the rest of the way and just one more bogey.
Northern Ireland's Rory McIroy (68) was third at 15-under 273, with Scotland's Paul Lawrie (71) and England's Barry Lane (67) sharing fourth place at 14-under 274.