Gay, Howell and rookie David Lingmerth each finished regulation play knotted at 25-under-par 263 after third-round leader Scott Stallings stumbled to a bogey on the final hole to miss the playoff.
Lingmerth fell out of contention when he bogeyed the first extra hole, while Gay and Howell each notched a par to advance.
Then, playing on the par-4 10th hole, Gay put his drive in the middle of the fairway and got to within 10 feet with his approach shot. Howell, however, found the rough with his first shot and a greenside bunker with his second.
After Howell failed to get up-and-down, Gay needed only one shot to sink a birdie putt for the win.
It was his fourth career PGA Tour victory and first since 2009.