GREENSBORO, August 18, 2013 (AFP) - The 23-year-old Reed rolled in a seven-foot birdie putt to beat fellow American Spieth who like Reed finished at 14-under 266 after 72 holes.
Reed's winning birdie came after his drive at the second playoff hole, the par-four 10th, landed in pine needles near a television cable.
He used a seven-iron to fire out under a tree branch and landed seven feet from the pin.
"It was the best shot of my life, that's for sure," Reed said.
Spieth called it "one of the best shots I've ever witnessed".
He had reached the green in two, but his 10-foot birdie putt was wide.
Reed said his birdie putt "felt like it was 40" feet, but it left him celebrating with his wife, Justine, who caddies for him.
"Just to get my first win means everything to me," Reed said.
Reed's first career victory came in his 38th start on the US PGA Tour.
The win also vaults him from 78th to 22nd place in the FedExCup standings with the tour's playoff series set to begin next week.
Reed had let a three-shot lead on the back nine get away. He also missed a chance to win at the first playoff hole, the par-four 18th.
Spieth made a terrible drive, but saved par with a 25-foot putt.
Reed, meanwhile, missed his seven-foot birdie attempt.
The 20-year-old Spieth won his first PGA Tour tournament last month -- also in a playoff at the John Deere Classic.
He was seeking to become the youngest two-time winner in US Tour history and he moved up to eighth place in the playoff point race with his runner-up finish.
Reed entered the final round in a tie for the lead with fellow American John Huh after he shot a one-over 71 in the third round on the soggy Sedgefield Country Club course.
Fearing more rain on Sunday, officials decided to send players off two tees in threesomes for the fourth round.
Reed, who had held at least a share of the lead since the end of the second round, carded a four-under 66 in the final round, while Spieth shot a five-under 65 Sunday.
Brian Harman (66) and John Huh (68) shared third place at 12-under, while Zach Johnson (68), Matt Every (67) and Matt Jones tied for fifth at 11-under.
Rory Sabbatini (65), Andres Gonzales (64) and Bob Estes (69) shared eighth at 10-under 270.
Leading final-round scores on Sunday in the US PGA Tour's $5.3 million Wyndham Championship (x-won playoff, USA unless noted, par-70):
266 - x-Patrick Reed 65-64-71-66, Jordan Spieth 65-66-70-65
268 - Brian Harman 67-66-69-66, John Huh 68-62-70-68
269 - Matt Jones (AUS) 65-71-71-62, Matt Every 67-67-68-67, Zach Johnson 67-68-66-68
270 - Rory Sabbatini (RSA) 67-66-72-65, Andres Gonzales 69-67-70-64, Bob Estes 67-66-68-69
271 - Webb Simpson 71-67-70-63, Jim Herman 67-66-72-66, Brendan Steele 71-67-66-67, Robert Garrigus 65-69-68-69
272 - Hideki Matsuyama (JPN) 70-65-71-66
273 - Henrik Norlander (SWE) 67-68-72-66, Martin Flores 67-72-71-63, Bryce Molder 66-69-71-67, David Toms 72-66-73-62
274 - Ernie Els (RSA) 71-68-70-65, Ricky Barnes 69-69-69-67, Bill Haas 69-66-71-68, Martin Kaymer (GER) 70-68-73-63, Park Jin (KOR) 67-69-70-68, Charlie Beljan 69-67-69-69
275 - Ryo Ishikawa (JPN) 70-69-69-67, Brendon Todd 68-68-75-64, Tim Clark (RSA) 69-70-72-64