The previous record was held jointly by Sally Little, Ayako Okamoto and Judy Dickinson. Okamoto shot her 65 on this course during the final round of the 1989 Open.
Alfredsson's score equalled the lowest round in a major championship by any golfer, male or female, and gave her a three-stroke lead over Patty Sheehan, Tammie Green, Dickinson and the amateur Carol Semple Thompson.
Alfredsson set the 54-hole record at the Open last year, but could only finish second by one shot. Her only victory since joining the LPGA Tour in 1991 was the Dinah Shore tournament in 1993.
She played a bogey-free round over the 6,244yd Old Course at Indianwood Golf and Country Club. Her only close call came at the last hole, where she drove into the left rough. But she hit her approach shot within 25 feet and two-putted for par.
'I wasn't really thinking about each shot needing to be perfect,' she said.
'It wasn't that hard. You wonder, 'Why can't I do this every day?'
Laura Davies was five shots off the lead, one of four players who shot 68.