Nick Dunlap held his nerve to become the first amateur to win a PGA Tour event since Phil Mickelson in 1991.
The 20-year-old hit a six-foot putt at the end to take the American Express title by one shot from South Africa's Christian Bezuidenhout.
It was his fourth PGA Tour event after missing the cut in the previous three.
“It's great to be able to experience this as an amateur,” the emotional American said after being embraced by his parents in California.
“Right or wrong, if you had told me come Wednesday night that I had the shot to win this tournament, I wouldn't have believed you.”
Mickelson, a six-time major champion, posted on X: “What a fantastic performance by Nick Dunlap. Congratulations on an amazing win.”
Dunlap is the seventh amateur to win a PGA Tour event, but his stock is already high after emulating Tiger Woods last year to become just the second player to win the U.S. Junior Amateur and U.S. Amateur titles.
His final round at La Quinta's Pete Dye Stadium Course featured a double-bogey six after he drove his ball into the lake on the 7th as he saw his three-shot overnight lead evaporate.
But the University of Alabama student responded in style with three birdies on his next nine holes as he closed with a one-under 70 to fend off a charging Bezuidenhout.
The South African, who fired a wedge shot from 138 yards for a two-under eagle in the 15th, also edged the latter in a seven-under 65 to set the club target at 28 under.
Dunlap, who moved to 29 under for birdie on the 16th, admitted he was unaware of Bezuidenhout's birdie on the final hole and when he was standing over his second-to-last shot, he thought he had a two-shot lead.
His approach leaked to the right and hit a spectator before accidentally coming to rest two yards from the edge of the green. He cut up to six feet and nervelessly punched the putt after his bearer told him “It's inside on the left, I've made a million of these before.”
Because he is an amateur, Dunlap will not receive any prize money, with the $1.5m (£1.18m) winner's check going to Bezuidenhout.
When asked if the natural next step was to turn professional, he replied: “I don't know. I have to take a moment to let what just happened sink in a little bit.”
“This decision is not just about me. It affects a lot of people, and obviously I'm going to try to enjoy this.”