They mastered the cold conditions on the Ocean Course at the Sky 72 Golf Club in Incheon to ensure a narrow advantage over another Korean, defending champion and world number six Choi Na-Yoen and Taiwan's Amy Hung.
A chasing pack of eight is a shot further adrift.
In that group is American starlet Michelle Wie, gunning for her third career title, along with Australia's Katherine Hull and Jimin Kang, who claimed a a thrilling one-stroke victory in Malaysia last Sunday.
Newly-crowned world number one Cristie Kerr stroked 71 to be three off the pace, along with fellow American and LPGA Hall of Famer Juli Inkster who was the runner-up last weekend.
Hurst, whose mother is from Korea, said she struggled in the cold weather at first but soon found her groove.
"It was really cold this morning. I thought that it was going to be warmer today, but standing on the putting green, I was really cold," she said.
"I just tried to keep warm starting out and stay steady because balls aren't going to be flying as far, and I probably won't be able to attack pins right away.
"I just tried to hit fairways, greens, two-putt, make pars and keep going and staying warm."
Co-leader Kim, who has been incredibly consistent over the past year or so but has yet to win a title, said it was a bogey she wanted to get off he back.
"It gives me some pressure, but it's not my last tournament," she said.
"I'm still young and will have a lot of chances to win. I will not be disappointed if I don't win this tournament. But one thing for sure is I will try to my best."
The tournament features the top 50 players from the LPGA money list along with the top 12 from the Korean tour.
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