Ko posted an eight-under 208 total with one round left, while Kim steadied after a double-bogey at the ninth to shoot a 73.
Kim played a bogey-free back nine, finishing in style by sinking a six-foot birdie at the last that left her only one stroke behind her fellow South Korean.
Another Korean, Lee Mi-hyang (68) was boosted by a hole-in-one at the 17th and jumped into a share of third with American Danielle Kang (70), three shots from the lead.
Ko surged to a four-stroke lead until disaster struck at the par-three 14th.
The 124-yard hole requires no more than a flick with a wedge, but Ko struck the ball a little fat and her ball failed to clear the pond guarding the green.
The resulting double-bogey gave renewed hope to her pursuers, who had been watching helplessly in the proverbial rear-view mirror as the Korean threatened to run away with it.
(Reporting by Andrew Both in Cary, North Carolina, editing by Nick Mulvenney)
