Third-ranked Suzann Pettersen of Norway bogeyed the last hole to fall one shot behind Miyazato, along with Hall of Famer Se Ri Pak of South Korea and Sandra Gal of Germany.
The 23-year-old Miyazato is looking for her first LPGA title this year, while Pettersen is in form after winning the Safeway Classic for the second time in three years earlier this month — her 12th Tour victory.
"The best part was my putting, because I (had) 25 putt(s) today," Miyazato said. "I think (it is) my best finish this year."
Pettersen had a chance to take the outright lead when her long birdie putt on the 18th hole hit the lip and rolled out, and she then missed an easy par.
Play was called off after less than an hour on Thursday due to heavy rain with the scores annulled, but it was sunny all day Friday at the tournament that is making its debut as the fifth and final major of the year.
That did not help top-ranked Inbee Park, whose bid to make golfing history got off to a bad start with a 3-over 74.
The South Korean is seeking to become the first professional golfer to win four majors in a season.
The 25-year-old Park double bogeyed the second hole and capped off a frustrating day with a bogey on the 18th.
She will have an even harder challenge now after the LPGA announced late Friday that it has decided to cut the tournament to 54 holes, having initially hoped to complete the 72 rounds by playing two rounds on Sunday, when rain is also forecast. There will be a 36-hole cut of the top 70 and ties.
But countrywoman Pak, who won the last of her five majors at the LPGA Championship in 2006, feels confident of challenging for another after improving her wayward putting.
The 35-year-old said "a bit of a lesson" from her father last week helped set her straight — literally.
"He knows me (better) than anybody," she said. "I was bending my upper body too much and at the same time my arms were too rounded."
American Christina Kim is two shots behind Miyazato in fifth place, and one shot ahead of teen star Lydia Ko, American Michelle Wie, and Australians Carrie Webb and Lindsey Wright.
Pak is 19 years older than Ko, the amateur from New Zealand who successfully defended her Canadian Women's Open title last month.
Pak made an even bigger impact in her first season as a professional in 1998 as the first two trophies of her career were both majors — the LPGA and the U.S. Women's Open — and she sees huge potential in Ko.
"When you play with the teenagers, they don't know much about the game, how to control the games. They just play golf, one day is a good day, one day is a bad day, very up and down," Pak said. "But she looks like she has her own game already, only 16 years old but she knew how to play, how to control."
No. 2-ranked Stacy Lewis, the only other player to win a major this year at the British Open last month, finished four shots back from Miyazato.
The course, built into the mountains in Evian-les-Bains overlooking the shores of Lake Geneva, is regarded as one of the best on the tour.
Over the past year, architects have undertaken a multimillion redesign focusing mainly on the four-hole finishing stretch. Formerly a reachable par-5, the 18th is now a par-4 and the new par-3 16th hole is played over water to a pitched green.