'Everybody can play out here,' said Thompson, who finished his round with an eagle on the par-5 18th. 'You don't get out if you can't play.'
Loren Roberts, making his first appearance at the tournament, opened with a 66. He was tied with Japan's Massy Kuramoto, who shared the lead with Thompson before a making a double bogey on his final hole, the par-4 ninth.
Tim Simpson, Scott Hoch, Joe Ozaki shot 67s.
Thompson, a three-time winner on the 50-and-over tour after also winning three times on the PGA Tour, had his first opening-round lead since the since the 2005 Bank of America in Boston. He won his last tour title in 2001.
'I'm invigorated to shot this round with my buddies at home much less out here,' Thompson said. 'If I shoot two more 64s I might win this thing. In fact, I'm predicting three 64s will win this tournament.'
He birdied hole Nos. 2, 5 and 7 for a 3-under 33 on the front nine. He played the back nine in 5-under 31, birdieing Nos. 10, 14 and 16 before his eagle on No. 18.
The 51-year-old Roberts missed his first opportunity to play the Austin event last year because of a family obligation, but was glad to make it this year.
'This might be one of the best courses we play all year along,' Roberts said. 'From the tee to green it was excellent, and I just had to get adjusted on the greens today.'
He was paired with Ben Crenshaw (73), giving the large crowd at look at two of the best putters in the world.
'I was trying to work on something with getting my swing more rounded so it was good at getting a look at a classic swing like Ben's,' Roberts said.
Kuramoto, who also eagled the 18th, said despite the late stumble, he was pleased overall with his game.
'After the rain we had earlier in the week, the course was very soft,' he said. 'After playing here last year, I feel like I know it much better.'
Defending champion Jay Haas, a five-time winner in Texas, shot a 71. He's coming off a victory two weeks ago in the Legends of Golf and also won the Toshiba Classic in March.