Thompson also won at TPC Wakefield Plantation in 2007 and 2011.
The 36-year-old former South Carolina player, making his second start of the season, won with a 4-foot birdie putt on the second hole of a playoff with Patton Kizzire and Miguel Angel Carballo.
Thompson holed his winning putt after Carballo missed from 30 feet and Kizzire from 7.
''I knew I had to make it to win,'' Thompson said. ''I thought, 'Just go through the same routine that I did 50 times this week. The putt's the same today as it was Thursday morning.'''
Thompson earned $112,500 to move into 15th place on the money list. He has four career tour victories, also winning the 2007 Oregon Classic.
''It means I get to keep playing golf for a living. It really does,'' Thompson said. ''If I miss the cut, I'm looking for a job. Literally, I'm at the end of my rope. Miracles happen. ... It's very emotional. I can't even put into words what it means to win this golf tournament. I kept my head down and kept doing the best I could. I had total belief that I was going to win this tournament, but I don't know where that came from.''
Thompson closed with a 4-under 67 to match Kizzire and Carballo at 17-under 267. Carballo birdied the final two holes for a 64. Kizzire finished with a 66.
Kizzire earned $55,000 to jump from fourth to first on the money list with $217,099.
Scott Parel and Drew Scott tied for fourth at 16 under. Parel had a 65, and Scott shot 68.