Starting the day tied for the lead with fellow American Zach Johnson, Landy charged out with birdies in his first three holes before parring the final seven to finish with a 17-under total of 271 at TPC San Antonio.
Trey Mullinax (69) and Sean O'Hair (66) tied for second on 15-under.
Chilean teenager Joaquin Niemann, the world's number one amateur before turning professional two weeks ago, finished sixth, five strokes behind Landry.
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Niemann birdied the final three holes for a 67.
"Today was a grind especially on the back nine. We'll take it," a relieved Landry said in a greenside interview.
The victory came three months after he lost a playoff to Spaniard Jon Rahm at the CareerBuilder Challenge in California.
Landry, 30, burst onto the scene at the 2016 U.S. Open, when he led after the first round. He finished 15th after playing the final round with eventual winner Dustin Johnson.
On Sunday, Landry had to work hard to stave off Mullinax, whose hopes diminished when he chunked a pitch shot at the 17th, failing to clear a bunker between his ball and the cup.
The resulting bogey gave Landry the gift of a two-shot lead heading to the par-five 18th, where there was still some suspense, after Landry's long birdie putt trundled eight feet beyond the hole.
That gave Mullinax hope of forcing a playoff, but he allowed for too much break with his nine-foot birdie attempt and had to settle for par. Landry had the luxury of knowing he could miss his par putt but sank it anyway.
He said his goal of qualifying for the season-ending Tour Championship, restricted to the top 30 players, had not changed.
"We still have a lot of work to do but this definitely helps," he said.
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond / Ian Ransom)
