Kim had a golden opportunity to claim her first career LPGA win on the final hole of regulation, but blew a 1-foot par putt, forcing a playoff.
The players returned to the 18th for the extra hole, and Yoo drained a 12-foot birdie putt. Kim couldn't respond, missing a 25-foot birdie effort and handing Yoo her first major championship.
She finished the round with a 3-under-par 69, ending tied with Kim (who also fired a 69) at 9-under 279 on the Dinah Shore Tournament Course at Mission Hills Country Club.
Top-ranked Yani Tseng, who was the co-leader after three rounds, managed a 1-over 73, finishing with sole possession of third place at minus-8.