The PGA Tour rookie, making his first appearance in one of golf's four biggest tournaments, claimed the early lead at the weather-affected U.S. Open on Friday.
His four-under-par 66 is the lowest first-round score carded at the tough Oakmont course in the nine occasions it has hosted America's national golf event.
The 28-year-old went one better than legendary duo Ben Hogan (1953) and Gary Player (1973), returning to the course early Friday morning to sink a 10-foot birdie putt.
It turned out to be his only shot of the day -- Landry will start his second round on Saturday.
"I'm going to go do some laundry and take a nap," the Texan said after carding his best score this season.
Ranked 624th in the world, Landry has missed six halfway cuts in 11 starts in his first PGA Tour campaign, with a best finish of 41st.
However, he is hopeful of a better result than that on a notoriously difficult course at a tournament known for its testing layouts.
"I like a golf course where par is a good score," Landry said. "I'm not going to overpower a golf course. No one is going to make a bunch of birdies (at the U.S. Open) and I feel like my game is so straight that I can hit it in tighter fairways."
Thunderstorms meant only nine players completed their opening rounds on Thursday.
Landry claimed a one-shot lead from more seasoned veterans Dustin Johnson of the U.S. and Englishman Lee Westwood.
Those two are still seeking their first major titles, but Landry may have a small edge -- his coach Chuck Cook has guided Tom Kite, Payne Stewart and Corey Pavin to U.S.Open victories.
"When he plays a course where par is a really good score, he tends to be in contention," Cook told the PGA Tour website. "He feels like he can win any tournament he gets into. He's always played tough."
Defending champion Jordan Spieth was six shots back after a 72 featuring four bogeys, while world No. 1 Jason Day suffered even more with a 76.
Third-ranked Rory McIlroy topped that with a 77, dropping shots at his last three holes on Friday, and the 2011 U.S. Open champion's playing partners fared little better.
Danny Willett, who won his first major at April's Masters, signed for a 75 while world No. 5 Rickie Fowler made 76.
Veteran Phil Mickelson, a record six-time runner-up in this tournament
, started his bid to complete his major collection with a 74.
Another U.S. Open debutant, 52-year-old Wes Short Jr., could not emulate Landry's fairytale beginning.
The American carded 78, with one triple bogey and another double.