Davies tied the course record set four years ago by Susie Redman.
Two-time champion Annika Sorenstam shared second place at 66 with Lynnette Brooky and Marta Prieto. Stephanie Arricau was alone in fifth at 67.
"I've been driving the ball magnificently all year," said Davies, 40. "But I really couldn't get anything going with the putter. I played very solid with only one bogey all day and that was my only bad putt all day. If I keep playing like that, I'll have my chance."
Defending champion Juli Inkster shot a 70. Michelle Wie had to settle for a 71, as did U.S. Women's Open champ Meg Mallon.
Celebrity Families of 2014 [PHOTOS]