Stallings had trailed by as many as five strokes Sunday, but forged a tie with Bob Estes and Bill Haas thanks to a birdie on the final hole. It was his sixth birdie on the final nine en route to a 1-under-par 69.
Stallings, Estes and Haas all ended regulation at 10-under 270 and headed back to the par-three 18th on The Old White TPC Course.
After all three found the green with their tee shots, Haas (67) two-putted for par, while Estes (64) ran his 12-foot birdie putt try past the cup, tapping in for par.
Stallings won it with a near-repeat of his final regulation-hole performance, draining the birdie putt for the victory.