The 23-year-old Woods is chasing one of three places available this weekend to qualify for next week's major at St Andrews.
Her 67 put her in sixth place, four shots behind joint leaders Caroline Masson, who carded a tournament record nine-under, and South African Ashleigh Simon, who only returned from a hip injury two months ago.
“I felt like I played really steady. One bogey, I felt like I hit the ball well so overall it was a good day,” said Woods, who celebrated her 23rd birthday on Thursday.
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