Kim Mi-hyun was in third, at 2 under.
In steady rain and winds of up to 24kph blowing in off the ocean, the Seaview Marriott Resort course was better suited for ducks than birdies.
But Inkster, a two-time champion and a consistently high finisher in the event, flourished in spite of the conditions, which left her hands feeling like prunes by the time she walked off the soggy 6,071-yard course.
Sorenstam, the tour's dominant player and a two-time winner here, overcame a sluggish start to reach 4 under.
Playing with a sore throat and stuffy nose from a nagging cold, she got into trouble early. She landed her tee shot on the 407-yard, par-4 second in a sand trap and then two-putted for bogey.
Mike Sullivan and Tom Jenkins played through windy conditions to shoot 6-under-par 65s for a one-stroke lead in the first round of the Allianz Championship.
Sullivan, a Champions Tour rookie who drives between tournaments in a 37-foot motorhome, had a bogey-free round and needed only one long shot for any of his six birdies -- a 25-foot chip just off the fringe on No. 8.
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