Money list leader Park had two eagles and also birdied the last to move ahead of overnight co-leader Suzann Pettersen (66).
The world number five, who won the LPGA Malaysia two weeks ago for her second victory of the year, took the outright lead despite the Norwegian producing a bogey-free round in Taoyuan County in Northern Taiwan.
Petterson, who won a play-off at the Hana Bank Championship in Korea on Sunday, had a hat-trick of birdies from the fourth to the sixth, and again from 13 to 15 to reach 16-under-par.
World number one and defending champion Yani Tseng is a further two shots back after a 68. She is two ahead of Scotland's Catriona Matthew.
Matthew, who lost on the third hole of that play-off to Petterson, went out in 32 but could only card a 68 at the Sunrise Golf and Country Club.