The Massachusetts-born 27-year-old had entered the final round with a one-stroke advantage after completing a third-round 64 earlier in the day in the weather-affected event.
And he held his nerve to post another solid round, picking up five shots - including late birdies on 16 and 17 to pull away - and only blotting his copybook with a bogey five at the 14th.
That gave Stallings a 24-under-par total of 264 - a tournament record at Annandale Golf Club - and a second PGA Tour triumph.
Jason Bohn signed for a flawless five-under 67 to stay in contention, but had to settle for second place.
Billy Horschel (71) was four shots off the pace in third, with Bud Cauley (66) a further stroke adrift in fourth.