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The 23-year-old American, sporting red and black golf clothing, suffered a wobble in the final nine holes but recovered to see off competition from Jamie Donaldson and Bubba Watson at Blue Monster.
Starting as overnight leader, he looked firmly on course for victory after opening up with three birdies in four holes.
But a bogey on the 15th left him just one clear of Donaldson as the tournament entered its final stages.
The Welshman couldn't capitalise, however, and made his first bogey of the day on the last to give Reed the breathing space he needed.
It was the American's third PGA Tour victory, having triumphed at the Wyndham Championship in August 2013 and the Humana Challenge earlier this year.
He began and finished the day on four under par overall, with Watson and Donaldson settling for a tie for second.
Tiger Woods, meanwhile, finished nine shots off the pace after a disastrous final round of 78.
The world number one, clearly hampered by his back injury, began with two pars but bogeys at the third and fourth undermined his challenge and another one at the sixth left him needing a miracle.
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