Stallings beat out Bob Estes and Bill Haas, who each posted par on the par-3 18th, to earn his first victory on tour and secure an invitation to the 2012 Masters Tournament.
Stallings was at 10 under until he hit his tee shot in the hazard at the 17th hole and went on to make bogey. But the rookie sank a 5-footer for a birdie at the 18th to join the playoff.
Estes, who has battled wrist injuries and missed the cut in five of his six starts this year, finished at 10 under first. He shot a bogey-free 65 in the final round and rolled in birdie putts of 4 and 15 feet on his last two holes.
Estes is a three-time winner on the PGA Tour. His last victory came at the 2002 Kemper Open, which was 223 starts ago.
Haas, who picked up his first two PGA Tour victories last year, closed with 67. He bogeyed the 15th hole but maded 10-footer for birdie at the 17th hole to tie with Estes.