Inkster, playing on her 50th birthday, shared the lead early in her round but suffered four late bogeys.
"I'm kind of disappointed in finishing the way I finished," Inkster said, "but I hit a couple of bad drives that got me in trouble."
Inkster won this event in 1999 and 2000.
Kerr, ranked fifth in the world, was the only Top 10 player in the rankings to break par. New world No. 1 Ai Miyazato, a winner four times on the LPGA Tour this year, struggled to a 76 and was tied for 97th.
Defending champion Anna Nordqvist, who has climbed in the rankings from No. 214 to sixth over the past year, shot a 73 Thursday.
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