Miyazato shot a 2-under 69 and was at 8 under with a round to go in the fifth and last women's major of the year.
The four-round tournament was cut to 54 holes after rain left the greens soggy. The course dried out somewhat Saturday but more showers are forecast for the final round.
Ko, who is 16 and plays with great composure, had four birdies in an error-free 4-under 67. Her only problem seemed to be her glasses, which did not cooperate in the weather.
"I'm having to clean all the time," she said. "I really want to get contacts. Cars have got wipers, they should design one for glasses. I would myself if I could."
Miyazato, whose day started with bogeys on the first two holes, is looking for her first U.S. LPGA title this year. Suzann Pettersen of Norway bogeyed her two holes on the back nine but had four birdies—as did Miyazato—for a 69 to share second with Ko.
"I didn't play my perfect game of golf out there, but I made a few really good pars," Pettersen said.
Ko successfully defended her Canadian Women's Open title last month, and her game has not lost any of its touch.
"I definitely gave myself a lot of opportunities," she said. "Hopefully it will be a good day tomorrow. But I can't hit it as good as I did today every single day.
Stacy Lewis, ranked No. 2, is two shots back in fourth after a 67. The American is chasing her second major title this season after last month's British Open.
Top-ranked Inbee Park faces an enormous task in her bid for golf history. The South Korean is trying to become the first professional to win four majors in a season.
She is 11 strokes off the lead. She opened with a 74 and followed with a 71 that included a double bogey on the fourth hole. She had to wait until the 13th for her first birdie of the day.
Three South Koreans—Se Ri Pak, Chella Choi and So Yeon Ryu—and Lindsey Wright of Australia are all three shots behind Miyazato. The oddest round of the day belonged to Sweden's Caroline Hedwall: two double bogeys, two bogeys, a hole in one on the 16th and seven birdies.
Organizers on Friday decided to shorten the major to 54 holes, having initially hoped to complete the 72 rounds by playing two rounds Sunday.
"I understand we're in a difficult position," Pettersen said. "It's not ideal for either the championship or for the players or for the tour in general to cut down on major rounds."
Some of the greens were expected to be covered overnight in a bid to optimize conditions. Lewis was unhappy about going to 54 holes and thinks the cut should have been shortened, rather than the tournament.
"I think a major should be 72 holes. I would have liked to have seen a cut to 50 instead of 70 and try to get 72 (holes) in," she said. "It's going to be muddy and wet. You just got to adjust and see what you can do."