After each player parred the initial playoff hole at No. 18, they moved to the 10th where Reed looked to be in trouble after driving into the woods as Spieth found the fairway at Sedgefield Country Club.
But Reed followed with a tremendous second shot from the trees to land within six feet of the pin and then sank the birdie putt for his initial PGA Tour triumph.
Reed, the co-leader after three rounds, registered a 4-under 66 on the final round to finish at 14-under 266, tied with Spieth (5-under 65).
Sharing third place at minus-12 were Brian Harman (66) and John Huh (68).
Wisconsin business offering 'therapeutic cuddling' forced to close
Reindeer recovered after escaping from Santa during lighting ceremony