The world's second-ranked golfer held a five-shot lead until he dropped six shots in three holes, culminating in a disastrous quadruple bogey on the short 12th, where he found the water twice.
It left Willett in charge and he duly increased his lead with a fearless birdie on the short 16th to go to five-under, a position he held until his triumphant finish.
Willett's bogey-free five-under round of 67 left him on five-under 283, three shots clear of Spieth and fellow Englishman Lee Westwood.
The 28-year-old came into the Masters as a four-time winner on the European Tour, but with an indifferent record in the majors, his best tied sixth in last year's British Open.
In his only previous appearance at the Masters last year he finished tied 38th and nearly skipped this year's first major with his wife Nicole due to give birth to their first child during the tournament.
The baby boy, Zachariah, was born last week, with proud new father Willett relaying the news on social media before heading to America.
At the presentation of the famed Green Jacket, Willett suggested that he was maybe destined to win.
"My wife was born in 10 minutes' time 28 years ago, my son was due today and born early to let me come and play -- talk about fate, it has just been a crazy week," he said.
Spieth, who won two majors last year and challenged strongly in the other two, has a remarkable record at Augusta, finishing second on his debut, winning in 2015 and leading for three rounds this year.
He looked set to become the first player since Tiger Woods in 2002 to defend the title, with the legendary Jack Nicklaus and England's Nick Faldo the others.
But after four straight birdies to the ninth, his round unraveled in astonishing style, bogeying the 10th and 11th and then slipping back to one-under with his travails on the 12th.
But Spieth is made of stern stuff and hit back with birdies at the 13th, 15th, only for a missed six-footer for birdie on the 16th to blunt his brave comeback.
He promptly bogeyed the 17th to fall back into a tie with Westwood after a closing one-over 73.
"It's tough, very tough," a crestfallen Spieth said as he reflected on his collapse. " It was a very tough 30 minutes that hopefully I will never experience again."
Sadly, there was no fairytale ending either for 58-year-old Bernhard Langer, who faded to a final round 79, while Spieth's partner in the final group, 24-year-old Smylie Kaufman, carded an 81.
The other action of note on the final day of the first major of the season saw an incredible three aces at the short 16th for first Irishman Shane Lowry, then American veteran Davis Love III and finally Louis Oosthuizen of South Africa.
Oosthuizen, who lost to Jason Day in the final of the WGC-Match Play last month, saw his tee-shot trickle down the green and nudge the ball of partner J.B. Holmes, which was already close to the flag, out of the way on its way to the hole.
They were the first holes in one at the tournament for three years.
England's Paul Casey, who matched Willett's last day 67, finished in a tie for fourth with American pair Dustin Johnson and JB Holmes.
Matthew Fitzgerald, like Willett from Sheffield in Yorkshire, also carded a 67 to finish level par in his second appearance at Augusta, the first in 2014 as an amateur.
The expected challenge from world No. 1 Day never materialized as he carded a 73 to finish on one-over, the same mark as third-ranked Rory McIlroy, both unable to maintain a sustained last-day challenge.