A runner-up each of the last two years, Ortiz hammered a 3-wood into the wind to set up a 20-foot eagle and a share of the lead, and he finished with two birdies for a 6-under 66 and a two-shot victory Sunday.
"It feels good to finally lift the trophy," Ortiz said.
The 23-year-old Ortiz earned a spot at Augusta National in April, and if he chooses to stay amateur, he will be exempt into the final stage of qualifying for the U.S. Open and British Open. He will be the first Mexican to play in the Masters since Victor Regalado in 1979.
Luis Gagne of Costa Rica, who plays at LSU, was tied with Ortiz with two holes to play on the Teeth of the Dog course at Casa del Campo. Gagne's tee shot on the short par-4 17th hole went into a bunker. Facing a 90-yard shot with a strong wind at his back, he went over the green and failed to get up-and-down.
Ortiz, in the final group behind him, decided against going for the green on the 295-yard hole. He hit 8-iron off the tee that bounced hard into light rough, and then pinched a 58-degree wedge that checked about 2 yards in front of the pin and rolled out to inches away for birdie.
Gagne missed a long eagle attempt on the par-5 18th and shot 66. Ortiz easily reached the green in two and tapped in for birdie to finish at 14-under 274.
A year ago, Joaquin Niemann shot 63 in the final round to beat Ortiz. The year before that, Toto Gana won a three-man playoff over Ortiz and Niemann. And when Ortiz fell two shots behind with seven holes to play, doubts began to creep in.
"I've been close so many times, I start to realize that maybe this isn't right for me, maybe I'm playing the wrong sport," Ortiz said.
But he remembered a text he received from his swing coach, who told him to "be your best friend today."
"I kept positive. I kept telling myself good things," Ortiz said.
He was between 3-wood and hybrid from 265 yards away on the par-5 12th when he opted for the 3-wood and hit it hard and high into the Caribbean wind.
"It came out like a rocket, and in the end, it floated," he said.
The eagle allowed him to tie for the lead, and Ortiz hit wedge from the rough to 3 feet for birdie on the 13th, while Gagne made birdie on the 14th to set up the finish.
Gagne made only one bogey on the weekend, at the 17th hole that cost him a chance to win.
"I hit a club I thought wouldn't get in the bunker," Gagne said. "I thought I was making the smart play. As you know, a 90-yard bunker shot, downwind, isn't the easiest. ... I'm extremely disappointed in the way I finished. Hypothetically, it could have cost me a ticket to the Masters. It will take me a while to get over this."
Ortiz, whose older brother Carlos plays on the PGA Tour, finished up his four years at Arkansas last year and decided to stay an amateur on the advice of his parents, who told him there was no rush. He played in the Palmer Cup and then decided to go through Web.com Tour qualifying as an amateur. The plan was to get through and begin his professional career at the start of this year.
"Gladly, it didn't work out," Ortiz said. "As soon as I missed second stage, my first thought was: 'This is my year. I'm going to win the Latin American and play in the Masters."
Ortiz says he and his brother dreamed about playing the Masters as teenagers in Guadalajara. He didn't imagine being the first of them to qualify. Carlos Ortiz would have to win a tournament before April to join him.
"For us Mexicans, we've been waiting for this a long time," Ortiz said. "It will be an honor to see the Mexican flag at the Masters. Hopefully, I'll do well and represent them well."