When Scheffler's final putt dropped on Thursday afternoon, he had a two-stroke lead over Rico Hoey of the Philippines and Jhonattan Vegas of Venezuela.
The World No. 1 is still seeking his first win of the year after racking up seven PGA Tour titles in 2024.
With eight birdies, an eagle and no bogeys a the TPC Craig Ranch, Scheffler put himself in prime position to break through in his home state for just the second time in his pro career.
Scheffler ran off four birdies in a row starting at the third hole. His irons and wedges were dialed in, as he put his tee shot at the par-3 fourth close to the pin and his approach at the par-4 sixth even closer.
He made an eagle at the par-5 ninth to go out in seven under 29.
Scheffler made just one birdie over the next seven holes before sticking his tee shot at the par-3 17th.
He had a 26-foot eagle putt at the par-5 18th that would have given him a round of 60, and it came up just a few feet shy.
Scheffler rocketed past Hoey, who had the early lead with an eight under 63 that featured an eagle and a run of five birdies between the second and sixth holes.
Tied at seven under 64 were Germany's Setphan Jaeger as well as the United States' Cameron Champ, Michael Thorbjornsen, Eric Cole and Andrew Putnam.
Jordan Spieth, a Dallas native like Scheffler, turned in a two under 69.
Karl Vilips was the best of the Australians in the field, finishing his opening round at six under and in a tie for tenth.
Aaron Baddeley was a further shot back and in a congested tie for 17th.
Scheffler missed last year's Byron Nelson for the birth of his son Bennett.
"Jordan (Spieth) and I love playing here. This tournament has meant a lot to us over the years," Scheffler said.
"Obviously last year I was missing for some pretty good reasons. I wasn't too sad about what was going on in my life at the time."
Back then, he had 10 wins combined before May over a three-year stretch, including the Masters and Players Championship twice each.
Not that he was playing poorly before posting his lowest round of the year. Scheffler finished fourth as the defending champion at Augusta and has four other top-10 finishes this year.
"I wouldn't say anxious or eager, anything like that," the 13-time winner said of his search for a win.
"I got off to a pretty good start today, and there's three more days of the tournament. Just focused on going home and getting some rest."
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