Sorenstam, the women's world No. 1, carded nine bogeys and just five birdies over her two rounds. She needed 65 putts to finish 36 holes, hit just 21 fairways and missed cut for the first time since the 2002 Women's British Open.
Coming off a one-week break following her fourth-place finish at the Ginn Clubs & Resorts Open, Sorenstam's streak of made cuts stood at 68 before Friday.
'I have to keep on grinding and keep on going,' Sorenstam added. 'That's really all I can do.'
Webb maintained the one-shot lead she held after the first round, shooting a 3-under 68 to move to 8-under-par 134 for the tournament. Defending champion Cristie Kerr fired a 5-under 66 to move into second place alone at 7-under-par 135.
Sorenstam played in a threesome with Webb and Kerr, who just tried to focus on their own rounds as the best women's player in the world continued to struggle.
'Obviously she was struggling a little bit, but I was just trying to keep to myself and try [to] play a little bit more solidly than I did yesterday,' said Webb.
Added Kerr, 'I've played with her enough to know that something was wrong. She was definitely not herself.'
Trailing Kerr by one shot was Pat Hurst, who shot a second straight 3-under 68 to get to third place at minus-6. Juli Inkster was one shot further back in fourth place after a 67.
Webb, who won the year's first major at the Kraft Nabisco Championship last month, followed up her 66 in Thursday's round with a solid effort Friday that included four birdies and one bogey.
She birdied two holes on the front nine to get to 7 under, setting up putts within 10 feet at the par-4 fourth and the par-4 eighth with a 6- and 7-iron, respectively.
Webb bogeyed the 10th when she two-putted from 10 feet, then played her final eight holes at 2 under to maintain the lead.
'I probably hit the ball better today than I did yesterday,' Webb declared. 'I just didn't make as many putts as yesterday, but it was a really solid round of golf.'
Kerr birdied two holes on the front nine, using an 8-iron to set up both birdies at the par-3 fifth and the par-4 ninth. She bogeyed 10 when she two-putted from 15 feet, then played her final eight holes at 4 under.
At the par-4 18th, Kerr rolled in a 30-foot birdie putt to secure her second place status.
'Actually, I had no idea what the putt was going to do,' Kerr said. 'I though I hit it too hard, but it went right in the middle. A 30-footer -- go figure.'
Reigning Women's British Open champion Jeong Jang shot a 70 and shares fifth place with Hee-Won Han (67) at 4-under-par 138.
Joo Mi Kim (68) and Meena Lee (71) -- already winners on tour this season -- lead a group of six players knotted in seventh place at minus-3.