Inkster overcame three bogeys with a trio of birdies to shoot even-par 72, heading into the weekend at 6-under-par 138 and looking for her eighth career major victory.
'Sometimes in a major championship you've just got to grind it out, and today was one of those days,' said Inkster, who fired a 66 Thursday. 'I'm very happy with the way I shot.'
'I just never hit it solid,' she admitted. 'It got me in a little bit of trouble, especially on the par fives where you need a birdie.'
Wie was assessed a two-stroke penalty for making contact with a piece of moss during her backswing in a greenside bunker at the par-4 14th, giving her a triple-bogey on the hole.
She wasn't notified until her round was over that what she thought was an even-par 72 was actually her second consecutive 74.
'I just could not get anything going, and it's not good after you play that you add two more shots,' said Wie, who is tied for 36th place at 4-over.
Wie was penalized because the rules specifically state that a player's club cannot make contact with a sand trap before the stroke. A stroke is defined only as the forward motion of the club.
'I knew I hit the moss, but I guess I knew the rule wrong,' Wie said. 'What I always knew from the rule ever since I started playing golf was that if you swing through it, it would be OK. It is a good learning experience.'
Wie drained an 8-foot birdie putt at the par-5 11th to get as low as plus-1 in her round. But she missed badly on a short birdie putt at 12 before botching the 14th.
Last year, of course, Wie was able to overcome an opening-round 75 with back-to-back 67s and a Sunday 69 to finish tied for third place at her first Women's British Open.
But at 10 stokes back heading into the weekend, Wie is in jeopardy of finishing outside the top-5 for the first time at a major this season.
Her infraction Friday was reminiscent of the one she made at last year's Samsung World Championship, where Wie was disqualified in her first professional start for taking a drop in the wrong place.
Wie, 16, joked Friday that the rule book is 'not actually great reading material.'
'[B]ut I am going to definitely call a rules official if something questionable happens,' she said.
Annika Sorenstam -- perhaps golf's biggest rule bookworm, man or woman -- is tied for seventh place at minus-1 following a 71. Sorenstam, the 2003 winner at Royal Lytham & St. Annes, opened with a 72 Thursday.
'A few missed shots out there makes it really tough because this golf course is so challenging,' Sorenstam said.
The world No. 1 finds herself missing opportunities on the same holes Inkster did Friday.
'I've been hitting the ball well,' Sorenstam said. 'I just haven't been capitalizing on the par 5s.'
Behind Inkster, Silvia Cavalleri is alone in second place at 3-under 141 after matching the leader with a 72. Cavalleri was tied with Inkster, but triple-bogeyed the 17th.
Lorie Kane and 2004 champion Karen Stupples both shot 69 and share third place with Candie Kung (70) and Lindsey Wright (71) at 2-under 142.
Tied with Sorenstam one shot further back are reigning LPGA Rookie of the Year Paula Creamer (71), leading Ladies European Tour player Gwladys Nocera (73), Il Mi Chung (71), two-time Women's British winner Sherri Steinhauer (70) and former champion Sophie Gustafson (67).
That's a lot of top-flight talent on Inkster's heels, but she has a milestone in her sights: the Super Career Grand Slam.
Only Karrie Webb has achieved what is called the Super Career Grand Slam -- winning the Kraft Nabisco Championship, the LPGA Championship, the U.S. Women's Open, the Women's British Open and the du Marier Classic, which was a major until it was replaced by the British in 2001.
If Inkster wins this weekend, she would become the second.
Technically, Inkster has already accomplished the Career Grand Slam by winning the first four majors she played (she completed it by claiming the LPGA Championship and U.S. Women's Open in 1999, the same year she became a member of the Hall of Fame).
Only the British has eluded her, with her best finish being a tie for 15th place last year.
Inkster, 46, could also become the oldest woman to win a major this weekend. (Fay Crocker was 45 when she won the Titleholders Championship in 1960.)
'I don't think age has anything to do with it. I just like to win,' said Inkster, who became the third-oldest woman ever to win a major when she claimed the 2002 U.S. Open at age 42.
'I've never won the British Open...But I've got to figure that driver out before I can even think about that.'
Webb, meanwhile, had a double-bogey and four bogeys Friday and shot a 10-over 82 to miss the cut at plus-14.
The cut line fell at plus-7 with 71 players advancing. Also missing the cut were Pat Hurst, Mi Hyun Kim and Carin Koch.
Se Ri Pak, the 2001 Women's British Open champion and reigning LPGA Championship winner, withdrew before the second round with a neck injury.