Three shots clear heading into the final round, Reed survived runs from Rory McIlroy, Jordan Spieth and Rickie Fowler to earn a green jacket when he bravely made pars at the final two holes.
"It's almost impossible to put into words," said the champion. "Just to make par on the last and to watch the ball go in the hole and know that I've won my first major. To finish off that drought meant so much to me."
McIlroy's early charge ended as quickly as it had started, but a sensational round from Spieth saw him tie the lead midway through the back-nine on his way to a 64 before Fowler asked the final question, birdieing the final hole to get within one.
But Reed had all the answers, scrambling his par at the 17th hole before finding the green with his approach to the last and safely negotiating a slippery two-putt for the title.
For Fowler, this was as impressive as he's been under the gun, the popular American making birdies at 12, 13, 15 and 18 to set a challenging clubhouse target at 14-under.
In the end it was not quite enough, as Fowler earned his third major runner-up finish and best Augusta result.
Spieth had appeared set to reach the same total until a poor drive and short missed putt at the final hole cost him a shot as he settled for third place.
It was a stunning run from the 2015 champion, who was five-under to the turn and added further birdies at 12, 13, 15 and 16 before missing an opportunity at the penultimate hole.
McIlroy was three behind overnight and soon cut that deficit to one with a birdie at the second hole, despite missing a short eagle putt.
But bogeys at the third and fifth put him on the back foot and he could never recover, dropping further shots at the par-five eighth as well as holes 11 and 14, all in clumsy fashion.
A share of fifth represented his fifth successive top-10 finish in the Masters, but this was the first time since 2011 that he'd traded as odds-on favourite and clearly represented an opportunity missed.
Meanwhile, Reed was able to bounce back from a poor stretch midway through the round as he carded a one-under-par 71, his worst score of the week but, in the circumstances, surely the best round of his life.
"I knew it was going to be tough, any time trying to close off a golf tournament is really hard but to close off your first major and to do it to a place that's so close to me being where I went to college..." he said.
"I knew the lead would shrink at some times, and the lead could grow - it's just the flows of golf, you have to know how to handle it and the way I could get that done was to make sure the putter was working."
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