South Korean star Kim played the first six holes in six under on Saturday before stalling at the tree-lined Sharon Heights course in California, leaving her with a five-stroke lead over American Nelly Korda as both shots six-under 66s.
World No.8 Kim was at 17-under 199. She won the tournament in 2015 in Phoenix for the second of her seven LPGA Tour titles.
Davidson shot a 69 to be tied for fifth at nine under with Robyn Choi (69) the next-best Australian a further shot back, while Minjee Lee (73) was at five under and Cassie Porter (72) at four under.
Four shots ahead entering the day, Kim had four birdies and an eagle on the par-5 fifth in the opening burst that ended with a bogey on the par-5 seventh.
Korda birdied 16 and 18 in a bogey-free 66. She skipped the Asia swing after winning the season opener in Florida.
Ruixin Liu of China and Gaby Lopez of Mexico were tied third at 11 under. Liu eagled the fifth in a 66. Lopez had a 68 playing alongside Kim.
Top-ranked Jeeno Thitikul (69) was nine under along with Davidson, Erika Hara (67), and Hye-Jin Choi (69).
The tournament began as a tribute to the 13 founders of the LPGA. It began in Arizona in 2011 and last year was the second event of the season and played in Florida.
It has attracted eight of the top 10 players in the world ranking and kicks off a four-tournament stretch in the West ahead of the first major of the year.
- with AAP
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