AP photo by Eric Christian Smith / Carlos Ortiz celebrates after closing his two-stroke victory at the Houston Open with a birdie on the 18th hole Sunday at Memorial Park.

HOUSTON — Carlos Ortiz never doubted he could win any golf tournament he entered, no matter the competition — even if he didn't have a single PGA Tour victory to prove it.

Now he does.

Ortiz holed two long birdie putts from off the green to take the lead at Memorial Park Golf Course, then was rock solid down the stretch as he delivered the winning shots for a 5-under-par 65 and a two-stroke victory Sunday in the Houston Open.

Ortiz played the final round alongside Jason Day, a former top-ranked player, and spent the back nine locked in a battle with Dustin Johnson, currently No. 1 in the Official World Golf Ranking.

The 29-year-old Mexican pulled ahead for good with a 6-iron shot so solid he started walking after it on the par-5 16th. Ortiz had to settle for a two-putt birdie from eight feet, but he finished his round in style with a 20-foot birdie for a 13-under 267 total.

Johnson (65) and Hideki Matsuyama (63), Japan's biggest star and a five-time winner on the PGA Tour, shared second place.

"I wasn't really thinking about the other guys. I wasn't worried," Ortiz said. "I knew if I played good I was going to be hard to beat. I knew I was capable of doing that because I know myself, but obviously validating that and then showing it, it definitely gets me more confidence."

Ortiz, a three-time winner on what was then the Tour in 2014, became the first Mexican to win on the PGA Tour since Victor Regalado at the 1978 Quad Cities Open.

Ortiz held back tears as he waited for his playing partners to putt. The victory sends him to the Masters next April. He was there a year ago to watch his brother, Alvaro, who qualified by winning the Latin American Amateur.

"This is like my second home," said Ortiz, who grew up in Guadalajara and played at the University of North Texas. "There was a bunch of people cheering for me, Latinos and Texans. I'm thankful for all of them."

It was the loudest cheer for a winner since March. The Houston Open was the first domestic PGA Tour event that allowed spectators during the COVID-19 pandemic, with 2,000 tickets sold daily.

They were treated to a good show, thanks in part to Johnson, who played for the first time since the U.S. Open after a positive coronavirus test forced him to miss back-to-back tournaments in October. After opening with a 72, he rallied with two rounds of 66 and was tied for the lead late Sunday, as was Matsuyama.

Formerly the final event before the Masters, the Houston Open was known as the last chance to make the field for the year's first major championship. A schedule shakeup last year moved the Texas tourney to the fall starting with the 2020-21 season, but it wound up being the last event before the Masters anyway when the major was postponed this spring because of the coronavirus.

The action at Augusta National starts Thursday in what will now be the final major of 2020.