Miyazato, who won last year's Q School, was tied for the lead with Kim until a disastrous double bogey at the 18th hole. She managed a 2-under 70 and finished 54 holes at minus-8.
Kim began the third round with a one-shot lead, but swirling wind wreaked havoc on play Saturday. She tallied her first birdie at the fourth when her 8-iron approach stopped 10 feet from the hole.
She added another birdie at the seventh when her sand wedge second finished six feet from the hole. Kim appeared to be in trouble at the par-5 10th when her third shot came up short, but the five-time winner on the LPGA Tour drained a long birdie putt from the fringe.
Meanwhile, Miyazato climbed up the leaderboard with strong play around the turn. She was even on her round, but a 10-foot birdie putt at eight got her to 1 under.
She two-putted for birdie at the par-5 ninth, then recorded back-to-back birdies from the 11th, thanks to a pair of spectacular 7-iron approach shots.
Miyazato bogeyed 13 thanks to an errant approach, but when Kim bogeyed the par-3 16th because of a poor tee shot, Miyazato was only one behind.
Miyazato cut the gap entirely at the par-5 17th. She laid up with her second then wedged her third to 16 feet. Miyazato converted the birdie try to pull even with Kim.
Things changed dramatically on the closing hole. Miyazato hit a relatively poor 9-iron to 32 feet, while Kim used the same club and landed her shot 3 feet from the stick. Miyazato four-putted for a double bogey and Kim sank her short birdie try to complete a three-shot swing, Kim's margin heading into Sunday's final round.
'I'm so happy I made birdie,' said Kim, referring to her putt at the last. 'When I turned around and looked at Ai, maybe she hit it too hard. You have to be careful on the short putts.'
Miyazato did not let her miscue at the last ruin her round.
'Everything went very well except for the last putt,' said Miyazato. 'I had a lot of fun today. Tomorrow is another day. I don't feel like this was the end of the world.'
Kim is looking for win No. 6 on the LPGA Tour, but she hasn't visited the winner's circle since the 2002 Wendy's Championship for Children.
'I'm just planning on doing my best,' said Kim, who found out just before her round on Saturday that her older brother had a baby boy. 'I just want to keep playing like today.'
Christina Kim shot a 3-under 69 on Saturday and is alone in third place at 6-under-par 210.
Karrie Webb, who won the season's first major at the Kraft Nabisco Championship, carded a 3-under 69 on Saturday. She is tied for fourth place with Seon Hwa Lee, who shot an even-par 72, at minus-5.
Lorena Ochoa, who lost to Webb in a playoff at the Kraft Nabisco Championship, was in second place after Friday's second round. She struggled to a 3-over 75 and is alone in sixth place at minus-4.
Pat Hurst (69), Lindsey Wright (69) and first-round leader Cristie Kerr (74) are tied for seventh place at 3-under-par 213.
Annika Sorenstam never got anything going on Saturday. She recorded four bogeys and two birdies en route to a 2-over 74 and a share of 15th place at even-par 216.
'I thought I played great,' admitted Sorenstam. 'You've really got to pay attention to the wind. It's making the greens putt firm and very, very fast. It's tough wind.'