The two golfers had started the day tied for the lead, then each shot 3-under-par 69s to end regulation knotted at 15-under 273.
Simpson would have won in regulation if not for a one-stroke penalty he assessed himself on the 15th green for grounding his putter.
Each drained birdie putts on the first extra hole and so were forced to play No. 18 again. This time, Watson's excellent second shot, which came within 50 feet of the pin, set up his match-winning birdie, earning him his second win of the year and third overall in his career.
Tied for third place at 13-under were Jason Dufner (66), Tommy Gainey (69) and K.J. Choi (69).
Sharing sixth one shot further back were Matt Jones and George McNeill, both of whom shot 2-under 70s.