Mizuno MP 53 Irons The American, 35, trailed Jordan Spieth by two shots after seven holes, but went three ahead by birdieing the 13th and parred the last five holes to win.
"I don't remember the last few holes," said Watson, who hit a three-under 69 to win on eight under.
"I just remember hanging on, making pars and walking up 18 was a little easier this time."
Ping K15 Driver "Jordan started out hot with a bunch of birdies, holing out of the bunker on four and hitting it really close on six, so for me to make birdies on top of him helped the momentum go my way a little bit," added Watson
Spieth, who was looking to become the youngest player to win the tournament at the age of 20, shared second place on five under with Sweden's Jonas Blixt after a closing 72.
TaylorMade RocketBladez Irons "It was so much fun, even if I did not show it on the back nine," he said.
"Although it stings right now I will be back and I can't wait to be back. That's what's on my mind because it's tough being in this position
"I've worked my whole life to lead in the Masters on Sunday, I had it in my hands and could have gone forward with it and didn't quite make the putts and that's what it came down to.
TaylorMade R11S Fairway Wood Watson missed a birdie putt on the last hole before beating South Africa's Louis Oosthuizen in a play-off to win his first Green Jacket in 2012.
He missed another birdie putt on 18 this year, but it mattered less given the lead he built up. Cameron Select Newport 2014
The momentum of the round changed when Watson birdied on the eighth and ninth, while Spieth bogeyed the same holes as the lead swapped hands.