Spieth, who had holed out from a bunker on the last hole to join a play-off, tapped in for par on the 18th hole to beat 2007 Masters champion Zach Johnson, who won last year, and Canadian David Hearn after the trio finished the regulation 72 holes tied at 19-under-par at TPC Deere Run in Silvis, Illinois.
Spieth, a two-time US Junior Amateur champion who began the round six shots off the pace, shot a final-round 65 and earned a spot in next week's British Open, an invitation to the 2014 Masters and membership on the Tour with the win.
"It's not settling in yet," said Spieth, who last year won a U.S. college championship with Texas. "It hasn't hit me yet. I'm not sure it will until maybe I wake up on the plane in a little while."
The win made Spieth the first teenager to claim a PGA Tour title since Ralph Guldahl won the Santa Monica Open 82 years ago.
"I don't think of my age as my age," Spieth said. "I just think of playing and competing with these guys as my peers. The guys in this event, each week, week to week, I don't think of myself as younger than them."
At 18-under-par, one stroke away from joining the play-off, were Martin Flores (63), Jerry Kelly (68) and overnight leader Daniel Summerhays (72), who overcame a string of four successive bogeys from the fifth hole.
Summerhays fought his way back into contention but failed to make the play-offs when he bogeyed the last after a brutal lie in a greenside bunker.
Playing on special temporary member status for his play in select events this year, which included five top-10s, Spieth put himself in position for something special when his greenside bunker shot on the last took one hop, hit the pin and dropped into the cup for a birdie.
Johnson came to the 18th holding a one-shot lead and looked poised to repeat as champion and notch his 10th tour title but bogeyed the hole to set up the three-way play-off.
The defending champion came close to winning the play-off when he lipped out a chip for birdie on the first extra hole and grazed the edge on another birdie putt.
Hearn, looking for his first tour title, missed two putts of about 10 feet, and Spieth had a 25-footer for a winning birdie on the first extra hole that died just short.
On the decisive hole, all three pushed their tee shots into the right rough, with Hearn having to thread a shot through a tight gap of trees and Johnson virtually stymied behind an oak.
Hearn came out short of the green, while Johnson deflected off a tree and into the water hugging the left side of the hole.
Spieth, who had the best lie of the trio, punched out of the rough and ran the ball to the fringe in back of the green, from where he two-putted for the winning par.
Tiger Woods, Phil Mickelson and Rory McIlroy all won their first PGA events at age 20.
"A year ago we had just won a national championship, and I thought I'd be back at school right now," said Spieth. "I had a plan. I guess the plan got exceeded.
"I wanted to just earn my Tour card for next year this year somehow. And now to be able to have it for a couple of years and to be able to have an exemption to Augusta (and) all the stuff that comes with it ...
"It hasn't hit me yet, and it will, but I'm just happy to go compete with those guys you mentioned."
- Sports & Recreation