Funk had 11 birdies and a bogey at Kapolei Golf Club.
''You've got to make a lot of birdies out here,'' Funk said. ''My putter came around. ... Never seen greens this good. They're pretty fast. They're pristine.''
Goydos shot a 63 to match Funk at 15-under 129. They broke the tournament 36-hole record of 13 under set by Bill Glasson in 2012.
Playing his fifth Champions Tour event since turning 50 in June, Goydos holed a 20-foot birdie putt on the par-5 first hole and closed with a short birdie putt on the par-4 18th.
''Making the putt on No. 1 was key for me,'' Goydos said. ''A good thing happened!''
Funk made seven birdies - most on short putts - in an eight-hole stretch from No. 4 to 12. He also bogeyed No. 8. He added birdies on the par-5 14th and 17th and closed with an 8-footer on 18.
''Today, was an exceptional day hitting close,'' Funk said. ''I've been playing well tee to green this year, but the putter has let me down. I switched putters this week.''
The 58-year-old Funk has nine Champions Tour titles, the last in June with partner Jeff Sluman in the Legends of Golf team event.
Pavin holed a 15-foot birdie putt on the par-4 18th. He also made birdie putts of 25 feet on No. 8, 15 feet on No. 10 and 25 feet on No. 16.
''I made some putts, finally,'' Pavin said. ''I've been working on working on it. It's nice to see some putts going in. I hit a really solid firm putt on 18. ... I like Hawaii a lot. When I come here it kind of puts me at peace. I feel relaxed here.''
Tom Pernice Jr., the first-round leader after a 60, was in the group at 12 under after a 72.