Karrie Webb (66), Angela Stanford (65), Leta Lindley (67) and Michelle Estill (68) are knotted in third place at 8-under-par 134.
Inkster, who won this title in 1999 and 2000, opened on the back nine Friday and birdied two of her first three holes. She parred her next four holes, then sank a 5-foot birdie putt at the 17th to go to 8 under par for the championship.
Inkster, who lives about three hours from the course, took her first lead at the first hole when she ran home an 8-foot birdie putt. She reached 10 under par at the very next hole when he drained a 2-footer.
At the fourth, Inkster had 45 feet for birdie, but ran her putt 5 feet past the hole. She missed the par-saving putt to fall back to 9 under and had an up-and-down finish to her round.
Inkster birdied the sixth, but dropped a shot to par at the par-4 seventh and in the process, fell into a tie for the lead with Kim, who was in the clubhouse at minus-9.
Inkster birdied No. 8 to go one clear of Kim and take her first 36-hole lead since the 2002 U.S. Women's Open, which she went on to win.
'Overall, I played well today,' said Inkster, who has won an LPGA Tour event every year for the last seven years. 'Even on my bogeys, I was in the fairway and had my chances. I hit the ball well.'
Inkster has four top-10s this season, but has not seriously contended for a title yet. She tied for second at the Michelob Ultra Open, but was two behind Se Ri Pak and needed several mistakes from the eventual champion in order to visit the winner's circle.
'I haven't given myself a chance to win,' admitted Inkster, referring to her 2004 campaign. 'It's about ball-striking and I am usually a good ball-striker. I haven't been this year, but I've been coming around.'
Kim, who held the first-round lead thanks to 64 on Thursday, failed to get anything going early on as she parred her first 13 holes. She hit a 4-iron left at the par-3 14th, then failed to save par.
She rebounded quickly when she reached the green in two at the par-5 15th. Kim, who is winless since joining the tour last season, two-putted from 60 feet for the birdie and got back to minus-7 for the tournament.
At the par-3 17th, Kim hit a 9-iron to eight feet to set up birdie. That same club helped her again at the closing hole when her 9-iron approach stopped 5 feet from the hole. She sank the putt to polish off a 2-under 69.
'Very boring,' said Kim, referring to her second round on Friday. 'It was such a long day out there. We had ruling, after ruling after ruling. You get into a lull and you can't be as sharp as you'd like.'
Kelli Kuehne fired a 5-under 66 and is tied for eighth place with Amy Hung, a Monday qualifier, who shot a 68 on Friday, and Miriam Nagl, who carded a second-round 70. That trio is knotted at 6-under-par 136.
The 36-hole cut fell at 1-over-par 143 and defending champion Helen Alfredsson missed the mark by one stroke. Among the other notable players who will not be around on the weekend are: Carin Koch (145), Sophie Gustafson (147) and Aree Song (148).