Texan Reed, 23, birdied the second extra hole to beat Jordan Spieth at Sedgefield Country Club and secure his first victory on tour.
Reed carded a closing four-under-par 66 to tie with Spieth (65) at 14-under 266, two strokes ahead of John Huh, who bogeyed the final two holes, and Brian Harman.
Spieth, 20, was gunning for his second victory in his past four starts, after his breakthrough at the John Deere Classic last month.
He almost became the youngest two-time winner in the modern era on the PGA Tour, but his runner-up finish nonetheless confirmed his status as one of the game's rising stars.
Spieth, who had to lay-up with his second shot after a wild drive, sank a clutch 26-footer for par at the first extra hole to keep the play-off alive.
He looked to have the upper hand at the second extra hole after Reed sprayed his tee shot almost out-of-bounds at the par-four 10th.
But Reed conjured up some magic, firing his second shot to seven feet and he sank the birdie to win after Spieth missed a10-footer that shaved the hole but stayed out.