Pernice, second behind Rocco Mediate two years ago at Broken Sound, hooked his drive into the water on the difficult par-4 ninth in the Champions Tour event. After a drop, he hit a 3-wood short of the green and missed a 9-foot putt.
"It's one of those things where you have to step up and hit a shot, and I wasn't able to pull it off," said Pernice, a two-time winner last year on the Champions Tour. "Not much you can do about it."
Bryant, playing alongside Pernice, had four birdies and an eagle. Goydos, a winner last year in his first season on the 50-and-over tour, had seven birdies and a bogey and saved par a half-dozen times.
"I probably turned a 69 or a 70 into a 66," Goydos said. "That's what I have to do to be successful out here.
Bernhard Langer was a stroke back along with Fred Funk and Tom Byrum. Langer, the reigning player of the year, won the 2010 event and has three other top-three finishes at Broken Sound in the last six years.
Defending champion Michael Allen had a 70, 10 shots higher than his opening round last year.
Nolan Henke had a 77 in his Champions Tour debut. The three-time PGA Tour winner turned 50 in November.