Every, seeking a first tour victory, had nine birdies in his flawless round on the demanding par-72 TPC San Antonio track and was three strokes in front of fellow American Hunter Haas.
Every's sparkling round vindicated his decision to forego coaches and limit his practice time.
He parted with his swing instructor a fortnight ago, and said he was taking a less-is-more approach to his tournament preparation.
"Lately I've been trying to do as little as possible with everything involved with golf," Every said. "If I'm hitting bad in the range I won't even work out -- I'll quit and go home. And it's been working. It has. I'm playing better golf because of it."
He said watching others tweak their games in search of better scores had only made him more sure of his decision.
"I see the same guys tinkering with their swings, and they spend all day Tuesday and Wednesday practising, and I think, 'God, I'm glad I'm not one of these guys,'" Every said. "And I'm sticking to that. When I get on the course, I'm more interested in playing golf than my golf swing."
Every is in the lead for the first time since January, when he shared the lead going into the final round of the Sony Open.
His wife, who is expecting a baby in two months, followed him for all of his round, which broke the previous course record of 64 shared by Ryan Palmer and Scott Piercy.
"I told her, only wanted her to go to nine today," Every said. "Said she had to keep going after the front nine. It's cool."
Haas posted one of the day's three eagles on the par-five 18th, where his three-wood from the fairway landed five feet from the pin.
It was an exclamation point to a bogey-free 66, and particularly welcome for a player who has missed the cut six times this season and finished no better than 37th.
"It's nice to finish a round like that. It's been a while," Haas said.
Former British Open champion Ben Curtis was in third after a 67.
It was a further shot back to Sweden's Fredrik Jacobson and Americans Cameron Beckman, Jason Gore, Troy Matteson and Derek Lamely on 68.
Matt Kuchar, the tournament's top-ranked player at No. 15 in the world, posted a 70 that finished with his bogey on the par-four ninth.
Leading first-round scores here on Thursday in the US PGA Tour's $6.2 million Texas Open (USA unless noted; par-72):
63 - Matt Every
66 - Hunter Haas
67 - Ben Curtis
68 - Fredrik Jacobson (SWE), Cameron Beckman, Jason Gore, Troy Matteson, Derek Lamely
69 - Rich Beem, David Mathis
70 - Matt Kuchar, Tommy Biershenk, Harris English, Kyle Reifers, Bud Cauley, Billy Mayfair, Miguel Angel Carballo (ARG)
71 - Vaughn Taylor, Stuart Appleby (AUS), Spencer Levin, John Rollins, Frank Lickliter, William McGirt, Mark Anderson, Kelly Kraft, Billy Hurley, Marco Dawson, Blake Adams, Ryan Palmer, Skip Kendall, Kevin Streelman, Garth Mulroy (RSA), Patrick Reed, Martin Flores