Juli Inkster, the eighth seed, birdied four of the final five holes, including a 4-footer at the 18th, to knock off Sorenstam, 1-up.
'It was very, very close,' said Sorenstam. 'She finished very solidly. I'm very happy with the way I played. I couldn't do much more. I wanted to give Juli the best match I possibly could.'
Wie was pummeled 4 and 3 by No. 39 Brittany Lincicome.
'I played very solid and just had a lot of bad breaks,' admitted Wie. 'There were a lot of wedge shots that could have been a lot closer and a lot of putts that could have gone in.'
Inkster will take on one of her partners from last year's Solheim Cup.
Paula Creamer, the fifth seed who played with Inkster twice in last year's biennial event against Europe, dispatched No. 4 Karrie Webb, 3 and 2.
Lincicome drew the LPGA Tour's leading money winner, Lorena Ochoa, in the semifinals. The Mexican, seeded third, overcame a front-nine deficit to knock off No. 27 Sophie Gustafson to the tune of 3 and 2.
The only close match was the last one between Sorenstam and Inkster, which was a rematch of the singles match from the 2000 Solheim Cup when Inkster destroyed Sorenstam, 5 and 4.
The Swede held a 2-up advantage after a win at the 11th, but Inkster came charging.
Inkster cut the margin in half with a two-putt birdie at the 14th. One hole later, Inkster rolled in right-to-left-breaking 10-foot birdie putt to square the match.
At the 16th, Sorenstam seemed to have the edge as her second stopped 6 feet from the cup. Inkster came up short of the putting surface with her approach, but chipped in for a birdie. Sorenstam holed the tester to move to the 17th even.
Both players narrowly missed long birdie putts at the par-3 hole, then both spilt the fairway at the 18th. Inkster went first and hit her second to 6 feet. Sorenstam followed with a 7-iron that came to rest nine feet from the flag.
Sorenstam's putt missed on the right edge. Inkster's poured right into the heart of the cup and now it's a semifinal match against Creamer, who is 27 years younger and grew up idolizing Inkster.
'I'm good friends with Paula,' said Inkster, who went 1-1 with Creamer last year at the Solheim Cup. 'She's fiery and she's going to be pumping her fists. I have to play my game and see what happens.'
Wie fell behind immediately as Lincicome captured the first hole. Wie squared it at the third, but Lincicome built a 2-up lead after five holes with wins at four and five.
Lincicome, who like Wie is one of the longest hitters in women's golf, took the 10th to move 3-up. Wie three-putted from 50 feet to lose the 13th and fall 4-down with five to play.
Wie gained a glimmer of hope when she sank a 12-footer for birdie at the 14th. Lincicome missed from 4 feet closer, but finished the match at the next hole after Wie took two to get out of a fairway bunker.
'I got up early and I kept the momentum going,' said Lincicome, who finished seventh at last week's U.S. Women's Open. 'I have been putting so well lately and that helped me win today.'
Next up for Wie is the John Deere Classic on the PGA TOUR next week.
'Hopefully I play as solidly as I'm playing,' said Wie, who has yet to make a cut in her previous experiences on the PGA TOUR. 'I feel like I'm playing awesome. Maybe a couple of lucky bounces here and there.'
Creamer took the fourth and fifth holes to move 2-up and Webb never mounted much of a charge. Webb did not win any holes until the 14th, when Creamer was already 4-up.
Webb, who won the season's first major, the Kraft Nabisco Championship, had a great opportunity at the 16th. Creamer short-sided herself in a bunker, then left her blast on the fringe, but Webb hit an awkward approach that landed short and right of the green.
Both made bogey and Creamer moved into the semifinals.
'I felt pretty good about it, but it's a shame I didn't get more out of it,' said Webb. 'I played pretty solid today, but just didn't make any birdies. I really screwed up on the last hole.'
Gustafson had the lead through much of the front nine, but Ochoa knotted the match by winning the eighth. She continued her strong play around the turn with wins at nine and 10 to move 2-up.
Gustafson cut it to 1-down with a win at 11, but Ochoa rolled in a 5-foot birdie putt to win No. 14. Gustafson was in a greenside bunker at 16 and thinned her blast 45 feet past the flag. Ochoa eventually won the hole and the match.
'I can only say I'm very excited to be here,' said Ochoa. 'I can't wait to be here tomorrow and I will do my best.'