Reed recovered from a drive on the par-4 10th that came a few feet from going out of bounds and stopped in some pine needles in the woods near a television cable.
Reed pulled out his 7-iron, uncorked a baseball swing from an uphill lie and sent the ball under a tree branch - yet away from the tree trunk - to land his second shot 7 feet from the pin.
''It was the best shot of my life, that's for sure,'' Reed said.
Spieth, who called it ''one of the best shots I've ever witnessed,'' had reached the green in two strokes, but his 10-foot birdie putt trickled wide of the cup.
Reed then sank his short birdie putt that ''felt like it was 40'' feet to end it.
''Just to get my first win means everything to me,'' Reed said.
Reed, who had his third straight top-10 finish, earned $954,000 in prize money and 500 FedEx Cup points for winning the final tournament before the playoffs.
Reed and Spieth finished regulation at 14-under 266. Reed closed with a 4-under 66, and Spieth had a 65.
The 20-year-old Spieth, the John Deere winner in a playoff last month, was denied in his bid to become youngest two-time champion in the modern era of the PGA Tour.
John Huh and Brian Harman were two strokes behind. Harman had a 66, and Huh shot 68. Matt Jones matched the tournament record for a final round with a 62 and finished at 11 under along with Matt Every (67) and Zach Johnson (68).
Reed - who let a three-stroke lead on the back nine slip away - missed a chance to win it on the first playoff hole, the par-4 18th.
Spieth recovered from a terrible drive and saved par with a snaking 25-foot putt.
Reed pushed his 7-foot birdie putt wide of the hole, sending it to a second extra hole.
''I don't even know how I was still playing (the second playoff hole) after what happened on 18,'' Spieth said.
Spieth and Huh both caught Reed at 14 under down the stretch in regulation.
At roughly the same time Reed bogeyed the par-3 16th, Spieth birdied the par-4 17th and closed with a par. Huh quickly slipped off the pace after finishing with two bogeys.
Reed, who led or shared the lead after the second and third rounds, also could have won it in regulation after landing his approach shot on the 18th in the center of the green.
But he left his approximately 20-foot birdie putt short and tapped in to force the playoff.
At the end of the day, the leaderboard looked much like it did at the start - tightly bunched. Eight players began the round within two strokes of the lead.
Reed compared the scenario to a Monday qualifier, and he knows plenty about those: he earned his spots in six tournaments last year by playing well in those 18-hole Monday rounds.
For the second straight day, organizers tried to beat the rain by starting the round early, sending players off in threesomes from the first and 10th tees. The skies were ominously overcast all day, but the saturated course didn't receive any rain.
And unlike the third round - in which only 13 players broke par - scores were significantly lower on the water-logged Sedgefield course, and that turned the final 18 holes into a shootout.
Jones birdied five consecutive holes and six of seven during his best round of the year.
''Every golfer out here can go and shoot that,'' Jones said.
Jones and Simpson, the 2011 winner who shot a 63, led the 52 players who shot better than even-par 70 during the final round.
''You really couldn't tell that the greens got any rain,'' Simpson said. ''They were still as fast today as I've ever seen them.''
At one point early in the round, five players - Reed, Every, Harman, Huh and Johnson - shared the lead at 10 under and six others were within two strokes of them.
It wound up being a mostly fruitless week for the players on the playoff bubble who missed their last chance to push their way into The Barclays next week.
Nobody who started the week outside the top 125 managed to make it in. Each of the players at Nos. 126-132 missed the cut, and No. 133 Robert Streb finished at 3 under but could only jump to 126th.
''I was trying to put (the pressure) to the side as much as I could,'' Streb said. ''You can't completely ignore it, but I just tried to play the best golf I could.''