Spanird Munoz shot an 8-under 64, including an eagle on the par-4 sixth and eight birdies on the Ko Olina course to raise her hopes of a first Tour victory.
Japan's Miyazato, a seven-times winner on the Tour, went round bogey-free to end the day level with Munoz.
"On six, I holed my second shot and then hit another two like that close," Munoz said, indicating the length of about a foot with her hands. "It was a really nice round."
Miyazato said: "My putting was really good today. I hit really solid on so many putts and I hit the ball well. I didn't miss any fairways. My short game was really good, too."
Jimin Kang and Cristie Kerr remained on the leaders' coattails at 6 under, after rounds of 66 and 68 respectively.
Yani Tseng, the world number one who has already won three events so far this year, suffered a poor day by her standards, shooting a 72 to drop to a tie for 12th at 3 under.
Michelle Wie's dire form continued as she missed the cut for a third straight event.