"I'm starting to play a little better. I'm starting to see the light at the end of the tunnel," said Price, winless on the 50-and-over tour.
Defending champion Scott Hoch was two strokes back at 67 along with D.A. Weibring, Fred Funk, Denis Watson and Tom McKnight.
Price made 15 Champions Tour starts last year after turning 50, with his best result a third-place finish in the Senior PGA Championship. This year, he has five top- 10 finishes in seven events.
"It's a strange game, really. I'm just glad to be out here and glad to see my game turning around," Price said.
Price made four straight birdies on Nos. 13-16, keyed by a 25-foot putt on No. 13.
"That really broke the dam," he said.
O'Meara also joined the Champions Tour in 2007, and while he has a couple of second place finishes, he's still looking for his first win.
"I was just trying to be patient and it paid off," O'Meara said. "I know these guys can play out here. You have to bring it every day."
He birdied Nos. 15 and 16 and made a 35-foot eagle putt on 18.
"That certainly was a nice way to end the day," he said.
Craig Stadler led much of the first round, tying a tournament record for low nine holes with a 31 on the front nine.