The 47-year-old Inkster, a 31-time winner on the LPGA Tour, matched South Korea's Shi Hyun Ahn (67) at 8-under 134 on the Royal Mayfair course.
'I hit some good short irons in there today. I drove the ball well, which is what you have to do out there,' Inkster said.
'You've got to play the ball from the fairway because of the rough. You can get some good lies in the rough, but you can get some gnarly lies. And depending where they put the pins, you just don't want to be coming in from the rough.'
Wie had a 7-over 149 total, leaving her 15 strokes behind the leaders.
'I missed a couple of crucial putts here and there and a couple of shots didn't go the way I wanted to,' said Wie, who had five bogeys and two birdies Friday. 'It's frustrating to see my score was high when I don't feel I played that bad.'
Wie, slowed by wrist injuries, also missed the cut two weeks ago in the Women's British Open at St. Andrews, shooting 73-80. The week before the Women's British Open, she tied for 69th in France in the Evian Masters, shooting 73-71-84-76 in her first start since withdrawing from the U.S. Women's Open because of a sore left wrist.
Ahn had a hole-in-one on the 157-yard 16th.
'I hit a 6-iron, a high draw shot and it went in,' Ahn said. 'Everything was good today. Shots were good. Putting was good. Everything was good.'
Top-ranked Lorena Ochoa (65), Kimberly Hall (67) and first-round leader Laura Diaz (70) were 7 under. Karrie Webb (64) was 6 under, and Paula Creamer (69) was another stroke back at 5 under. Defending champion Cristie Kerr (70) was 3 under.
'I think I missed maybe one fairway and it was on the first cut, and that makes a big difference,' Ochoa said. 'I think the course was a little bit more difficult because of the variation of the wind. Some holes changed. We had to be careful with the tee shots. I played more with my 3-wood today than my driver and it worked, so I think I'm going to try to do the same on the weekend.'
The Mexican star won the Women's British Open for her first major title and leads the tour with four victories this season.
'She's got the momentum going right now,' Inkster said. 'She's on fire. She's kind of like the way Annika (Sorenstam) was three or four years ago, when we knew coming in you were going to have to have you're `A' game to compete with her.'
Longtime Canadian star Lorie Kane missed the cut with rounds of 75 and 77.