The 35-year-old from Portland stormed up the leaderboard with a seven-under-par final round of 63 at Sea Island.
Simpson earned a play-off by joining his fellow American on 15 under with a blemish-free 66, but missed a three-foot putt for par on the second play-off hole - the 17th.
Two major winners from South Africa rounded off the top five, 2010 Open champion Louis Oosthuizen 13 under after a 66 and 2008 Masters champion Trevor Immelman a shot further back following a 69.
Two-time major winner Angel Cabrera of Argentina finished 10 under and tied for sixth after a 67 along with American trio Scott McCarron (68), Kevin Streelman (68), Jeff Overton (69) and Australia's Nick O'Hern (69).
Rookie Michael Thompson had looked on course for his maiden PGA Tour triumph when he opened up a three-shot lead with three birdies over his first six holes.
The 26-year-old from Tucson birdied three straight holes from the fourth and was 16 under through seven, but that was as good as it got and two bogeys on the back to a third-place finish on 14 under.
Billy Horschel, who was just one shot behind overnight leader Thompson at the start of play, opened well with birdies on one and three but endured a nightmare round thereafter.
A triple-bogey seven on the par-four fifth and a double bogey on 18 - along with further dropped shots on four, seven and 15 - saw him slip to joint 20th after signing for a five-over-par 75.