Johnson, who started the day three shots behind overnight leader Spieth, set himself up with a monster drive at the first playoff hole and finished off the win with a three-foot birdie putt.
He had tucked his approach in close for an almost-certain birdie, so the writing was on the wall when Spieth was unable to make his long birdie attempt from the fringe.
The two stars had dueled down the back nine at Glen Oaks Club in Old Westbury, New York.
Johnson drained a 17-foot downhill putt for par at the 72nd hole of regulation to force the playoff, and then claimed his first victory since a back injury suffered in a fall forced him out of the Masters in April.
Until the injury, he'd been on a roll in 2017, winning three tournaments to ascend to the top of the rankings.
"I feel the game's finally back in form like it was leading into the Masters," Johnson said. "I'm swinging everything really well, got a lot of control over the golf ball and I'm feeling really good.
"Getting a win here today gives me a lot of confidence going into next week and the rest of the playoffs."
He fired a final round 66 on Sunday for 13-under 267 in the first of four events in the US PGA Tour's FedEx Cup playoffs.
Spieth closed with a 69. The leading duo were four shots in front of Venezuela's Jhonattan Vegas, who carded a 65 in the final round, and Spain's Jon Rahm, who signed for a 68.
Spieth was in control most of the day, and led by as many as five on the front nine.
But he and Johnson were tied for the lead heading to the par-three 17th, where both were in a bunker.
Johnson blasted out to within four feet of the hole. Spieth's shot skipped 18 feet from the hole -- but he stepped up and made the putt to stay tied.
At the next, Johnson was in dense rough off the tee and opted to lay up, leaving him his testing par putt as Spieth two-putted from 75 feet for par.
"I thought that was a fun show," Spieth said of the back-nine duel. "I was hoping it wasn't going to be that much fun."
Spieth opened the door with a double-bogey five at the par-three sixth hole, where he was in the water off the tee.
He bogeyed the ninth before a blemish-free inward run that included back-to-back birdies at 13 and 14.
"I didn't lose the tournament," Spieth said. "He won it."
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