Ranked 218th in the world, Potter overcame a four-stroke deficit with four holes to play, finishing with his second straight 6-under 64 to match Kelly at 16 under. Kelly closed with a 66.
Potter became the sixth first-time winner on the tour this season. He earned $1,098,000 and jumped from 173rd to 51st in the FedEx Cup standings.
The 28-year-old left-hander had missed five straight cuts entering the Greenbrier Classic and his previous best finish was a tie for 13th.
Charlie Wi and rookie Charlie Beljan tied for third at 14 under. Wi shot a 65, and Beljan had a 67.