The 2008 US Women's Open champion tamed the Mission Hills course with a 67 for the second day in a row to surge to 12 under par.
That put her comfortably ahead of her nearest challenger, American Lizette Salas, who herself held a three-shot cushion over a group of six players tied for third on six under: Norway's Suzann Pettersen, US players Angela Stanford and Jessica Korda, Australian Karrie Webb, France's Karine Icher and Thailand's Pornanong Phatlum.
Stanford signed for a best-of-the-day six-under 66 at the California course, and anyone hoping to challenge 24-year-old Park over the final 18 holes will almost certainly need to shoot similarly low.
Korda, who carded a 68, is the daughter of former tennis grand slam winner Petr Korda, who triumphed at the Australian Open in 1998.
"I was there," said Korda, who would have been aged four.
"I was in the stands. I had this purple notebook that I was drawing in and had no idea what was going on. But I do remember him like climbing up the wall and running up to me and my mom and lifting me up and saying that he won.
"So I definitely remember certain aspects of it, not the whole thing, though."
With his experience as a top-level sportsman, Czech Korda has been able to pass on some wisdom to his daughter, who turned 20 in January and has played under the US flag for several years, having been born in the country.
Petr Korda is around this week, playing a supportive role.
"I think he tries to be just Dad, but the athlete in him always wants to help, and I appreciate any help I can get from him because he knows so much," Korda said.
"He's just been telling me to have fun, just relax and smile and enjoy it."
British hopes of success were dashed when first-round co-leader Jodi Ewart Shadoff, who had remained in contention after a level-par second round, fell away to a share of 17th place on two under after a two-over 74.
The Englishwoman was one shot ahead of Scotland's Catriona Matthew who had her best round of the week, a two-under 70.