Park, who won the 2008 US Women's Open, moved to 14-under-par overall with the five-under round, and stretched her lead to two shots over Brittany Lang (67) and Hee Kyung Seo (67).
"I haven't had a win for a while, so it [would] be nice to win tomorrow," Park said after her round. "But I'll just go out there, just play like today with no expectations, just play like a normal day."
The tournament caught up after losing time in the first two days to weather delays.
Lurking lower down the leaderboard, world number two Stacy Lewis is eight-under-par after three rounds, on the same score as talented teenager Lexi Thompson.