He carded a closing 65 at the Colonial Country Club in Fort Worth for a 17-under total of 263, good for a three-shot cushion over fellow American Harris English (66).
“To come back in only our third tournament and close it out is really, really special,” Spieth said.
“I’m already looking back, thinking this will be a very important day to get back on top and be in the winner’s circle.
"As a golfer and as a person I can always look back on this experience and say we were strong in what shouldn’t have been tough times, but were tough times.”
Only the late Horton Smith, with 14, recorded more wins than Spieth at 22 or younger.
Spieth, the world number two, opened with three straight birdies on his back nine and closed with three straight birdies. On his final three holes, he curled in a 20-foot birdie putt, chipped in from 40 feet and punctuated his performance with a 35-foot putt on the closing hole.
He also received a little help from the golfing gods. With a one-stroke lead on 17, Spieth received a break when his pulled tee shot glanced off the leg of a marshal and finished in the first cut of rough. He drilled his approach shot over the green and received a free drop from a grandstand.
“Seventeen was one of the luckiest holes I’ve ever had personally,” Spieth said.
“I hit a guy in the side and it goes in the first cut, get a drop and chip in. If I’m playing against me I’d be pretty upset.”
Spieth began the final round with a one-shot lead and had to withstand an early charge from English, who knocked in his 83-yard approach shot for eagle on the par-five opening hole.
Spieth, who also made lengthy par putts at eight and 14, became the first Texan to win the Colonial since Ben Crenshaw in 1990.
He understands why golf fans and media have talked at length about his performance at the Masters, where he threw away the green jacket with a quadruple-bogey at the 12th hole during the final round.
But Spieth kept telling himself over the ensuing weeks to tune it out the incessant babble.
"Don't listen to the noise," he told himself.
(Reporting by Tim Wharnsby in Toronto; Editing by Andrew Both)
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