Watney, who entered the day behind third-round leader Dustin Johnson, ended at 16-under 272. He avoided a playoff when Johnson missed an eagle by just 5 feet with his approach shot on the 18th hole.
Watney grabbed the lead with a sizzling stretch in which he carded four birdies and a bogey, beginning with No. 8.
Johnson, meanwhile, had trouble putting Sunday and managed only a 1-under 71 in the final round, falling into second place at minus-14.
Anders Hansen (67) and Francesco Molinari (69) ended in a third-place tie at 13-under-par 275 on the TPC Blue Monster at Doral.