Alfredsson's three-day total of 207 - nine under par - was a tournament record and she needed a one-under-par 71 in the final round to break Pat Bradley's record of nine under, established in 1981 at the La Grange Country Club in Illinois.
Alfredsson, whose only previous LPGA victory was in March at the Dinah Shore, bogeyed the par-three sixth hole but came back with birdies at seven and eight, both par fours, and an eagle three at the ninth, a 435-yard par five where she hit a driver and four-iron within five feet.
On the back nine she birdied the par-three 17th and bogeyed 10 and 18, both par fours. 'I was striking the ball well,' Alfredsson, 28, said afterwards. 'Seven, eight and nine was really what helped my round.
'What I have learned in majors is that you have to have patience. You can't get frustrated with one shot and feel like you've let it get away.'
Kobayashi, the 30-year-old who picked up her first tour victory last weekend, shot 71 for a 209 total.
Bradley, who is still seeking her second Open championship 12 years after her record performance, recorded the day's best round - a four-under-par 68 - to move into a third- place tie with her fellow American Donna Andrews, who shot a 69.
One shot back in a group of three, with the first-round co-leader Ayako Okamoto of Japan and the tour rookie Dina Ammaccapane, is Nancy Lopez, the American still seeking her first US Open. Two behind those three is Britain's Laura Davies, who shot a third-round 69.
Scores, Sporting Digest, page 27