"I really jump-started my round with a save on No. 2," Funk said. "I drove it into the bunker and had to wedge it out for par. Then I made a 30-footer (putt) on the next hole (for birdie), and that got me going."
The winner at The Woodlands in Texas in May for his seventh Champions Tour title, Funk has gone 42 holes without a bogey since the 13th hole Sunday in the final round of the SAS Championship in Cary, N.C.
He also extended his run of bogey-free holes at Rock Barn to 66, beginning with the seventh hole of the second round of last year's tournament.
"I've missed quite a few chances where I could've had more birdies," said Funk, who has 10 birdies and an eagle in two rounds. "I've played pretty solid ... but I'm not going to complain about a 66."
Funk had six birdies Saturday, but spent most of the day tied with Mize for the lead until draining a 20-foot birdie putt on No. 18.
"My only goal is to go out there, let it happen and not force the issue," said Funk, who shot 62 in the final round of last year's tournament to finish second. "Someone can get on a run, because the greens are a lot faster and rolling really true. The scores are higher than they were last year."
The 54-year-old Mize, a former Masters champion whose lone Champions Tour win came in 2010 in the Montreal Championship shot a 67.
"I played pretty solid yesterday, and I played pretty solid again today," said Mize, who overcame a bogey with six birdies, including three straight on Nos. 12-14. "Obviously, I have to keep this up. Fred's going to be tough, and there are other guys out there as well."
Defending champion Mark Wiebe, Chip Beck and Duffy Waldorf were four strokes back at 8 under. Beck and Waldorf shot 67, and Wiebe had a 69.
First-round leader Dan Forsman, struggling with back problems, was 7 under after a 72.