Reed went into the final day with a three-shot lead and was bidding to become the first Masters champion to record four rounds of under-70, but the American struggled to replicate his performances from the first three days.
Compatriots Rickie Fowler and Jordan Spieth piled the pressure on the leader with rounds of five-under and eight-under respectively, with Spieth's 64 almost seeing him pull off one of the great Masters comebacks to regain the title he won in 2015.
Reed hit three bogeys during his round of 71, but crucially followed each of those with a birdie and ultimately a fourth birdie of the round on the 14th proved to be enough for him to claim the green jacket.
The 27-year-old ended on 15-under for the tournament, while Fowler's score of 14-under means that he has now finished second at the US Open, The Open and The Masters in his search for a first Major.
Tiger Woods recorded a final-round 69 to finish with a flurry - including an eagle on the 15th - but the four-time champion still ended the Masters on one-over par.