Lowery settled for a birdie at the 190-yard 13th after his 6-iron lipped out, then holed out from the fairway from 168 yards with an 8-iron for an eagle on the next hole.
This is the first year the event has been played at TPC San Antonio's Canyon Course, and more than half the field shot under par. There was hardly a breeze on a nearly cloudless day over a Pete Dye-designed course that doesn't look anything as demanding as his layouts in places such as Whistling Straights or Kiawah.
"I think this had to be the prettiest day we've played golf all year long," said Sutton, who hit all 18 greens in regulation. "If you hadn't have told me Pete Dye (designed the course), I wouldn't have really guessed that."
Defending champion Rod Spittle (74) was among the 31 players over par.
Couples is playing for the third straight week and is looking for his third-straight top-10 finish despite back problems that have been eased by protein injections he received this summer in Germany. He won the Senior Players Championship in August and tied for 15th at the Masters.
"I feel pretty good right now," Couples said. "But I'm not going to overdo it."
Though he birdied his first three holes and had eight for the day, he got big breaks with a 30-foot putt for par on the No. 8 and then saw his errant drive at No. 12 hit a rock and bounce back into the middle of the fairway. He birdied.
"Little jumps like that are big moves," Couples said.
Lowery, who's victory at the AT&T Pebble Beach Pro-Am three years ago is one of his three victories on the regular tour, is looking for his first trophy on the Champions Tour. He would have come in with the lead if not for a bunker shot at No. 17 that clipped the lip of the trap and barely dribbled onto the green. That left him 90 feet from the cup, and he three-putted.
It's the last full-field tournament for the Champions Tour before the top 30 in the point standings head to the season-ending Charles Schwab Cup at Harding Park in San Francisco in three weeks.