Overnight leader Ko had been cruising through her round having picked up four birdies in her first six holes only to make back-to-back bogies on the 11th and 12th.
A birdie four seemed to have put her back on track only for the 18-year-old to find a water hazard on the next en route to a double-bogey six.
The New Zealander, the youngest winner of a golf major, was able to eventually fire a three-under-par 69 after collecting two birdies over the closing stretch to join home favourite Park at the top of the leaderboard.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Park, who has three wins on the Korean Tour and is chasing an LPGA Tour card with a strong finish this week, had a far less eventful round, dropping only one shot in her five-under-par 67.
The 22-year-old long hitter recovering well after a disappointing 74 on Friday to follow up a course record 62 to start the $2 million tournament.
Thailand's Moriya Jutanugarn was tied fifth on 11-under after a 67 alongside another Korean Cho Yoon-ji (69).
Former world number one Yani Tseng of Taiwan was a further shot back in seventh after recovering from a double bogey five at the third to shoot a 69.
(Writing by Patrick Johnston in Singapore; Editing by John O'Brien)
