After an opening 65, Miyazato recovered from bogeys at her first two holes yesterday to add a two-under-par 69 thanks to birdies on the sixth, seventh, 13th and 18th.
That put her on eight under overall, one ahead of Norway's Suzann Pettersen (69) and teenage amateur Lydia Ko with world No 2 and Ricoh British Women's Open champion Stacy Lewis a shot further back.
Pettersen, one of the stars of Europe's Solheim Cup win in Colorado, said: "It wasn't a perfect round of golf but I managed to put a score together and give myself a chance for tomorrow.
"I made a few key pars and tried to take advantage of good playing conditions. There were a few tricky pin placements as well, so it's not that easy to get four or five under."
Ko, 16, has already won five professional titles, including retaining the Canadian Open. She returned a flawless 67 which featured birdies at the third, fourth, 17th and 18th.
Lewis added a 67 to her opening 69 and then expressed her disappointment at the early decision to make it a 54-hole event.
"I think a Major should be 72 holes," the American said. "Reducing it to 54 makes it a shoot-out, so you just have to go out there tomorrow and do the best you can."
Inbee Park's bid to become the first player to win four Majors in the same year looks to be over after the South Korean could only add a 71 to her opening 74. Scotland's Catriona Matthew just made the cut after a second 73 left her 11 shots off the pace.
On the men's European Tour, Holland's Joost Luiten rewarded the home fans for braving some miserable conditions by claiming a narrow lead after the third round of the KLM Open at Zandvoort.
Luiten carded a four-under-par 66 for a 10-under-par total, one ahead of overnight leader Miguel Angel Jimenez who battled to a level-par 70.
Ireland's Damien McGrane shot 67 to move into a share of third place on eight under alongside France's Julien Quesne, with three-time winner Simon Dyson and fellow Englishman Oliver Fisher a shot further back after matching 71s.
Scot David Drysdale, sixth after shooting 64 on Friday, had a day to forget as he slipped down the leaderboard following a 74.
At the Russian Open on the Seniors Tour, Colin Montgomerie, looking to capture a second victory in successive starts after his triumph at Woburn two weeks ago, shot an excellent 67 to sit just two shots behind the leader, England's Simon P Brown.