Kim, forced into a playoff with Hall of Famer Juli Inkster because of the miss, won on the first extra hole - making a 4-foot par putt on No. 18 - for her first LPGA Tour victory of the year.
Kim, who started the round one shot behind the leaders, won for the eighth time on tour. Inkster, who will turn 47 next month, would have been the oldest player to win an LPGA Tour event. She closed with a 2-under 69 in regulation.
Kim, who shot a 71, and Inkster finished regulation tied at 3 under, one shot ahead of Ai Miyazoto and Angela Stanford. Four others were at 1 under, including Lorena Ochoa, Reilley Rankin and Stephanie Louden. Rankin and Louden began the day in a four-way tie for first.
"My goal is just top 10, top 20 this week," Kim said. "I never (thought) about a win this week. Maybe I worry about the cut."
Kim, whose last tour win in 2006 came after a three-hole playoff with Natalie Gulbis in the Jamie Farr Owens Corning Classic, hit her second shot in the playoff to the fringe on the back of the green, about 35 feet from the hole, and two-putted.
Inkster's second shot, using a 6-iron, sailed over the green. She chipped 8 feet past the hole but missed the par putt.
"I don't know if it was adrenaline or what, but I just hit it too far and didn't get it up and down," Inkster said. "Kind of disappointing.
"I've been putting good. I just felt like if I could get it within my reach, I could make it but it didn't happen."
Six players held the lead at some point on a cloudy, humid day. The 6,602-yard Cedar Ridge Country Club course was soggy from storms that hit Oklahoma the past week.
Moments after Inkster bogeyed No. 17 to fall out of the lead, Kim curled in a breaking 15-foot birdie putt at 16 to take a two-shot edge. Inkster hit a 6-foot birdie putt on 18 to close the gap to one shot.
Kim hit her tee shot into the rough on the par-4 17th, but salvaged par, knocking a 5-foot putt into the center of the hole. On the 18th, her tee shot landed in the middle of the fairway but she hit into a greenside bunker and two-putted for bogey.
"After the bunker shot, I was so excited and nervous, so my hands were shaking," Kim said. "So when I marked the ball, my hand was shaking. So when I set up the putt, I know the line, but I can't stroke the putt."
She said she wasn't nervous during the playoff, because at that point, "You have to get more lucky. Juli's second shot was over the green, that was unlucky (for her). But that was lucky for me."
The round started with four co-leaders - Nicole Castrale, Rankin, Louden and Karin Sjodin - who had not won on the tour. One by one, they all fell back. Castrale, who led after the opening round, was still at 4 under through five holes, but bogeyed four of the next eight. Louden had four bogeys in her first six holes. Sjodin, who played at nearby Oklahoma State, was tied with Inkster for the lead after a 3-foot birdie putt on No. 6, but big trouble followed on the 405-yard, par-4 eighth hole. Sjodin's drive went into the deep rough and rolled into a ravine to the right of the fairway. Instead of trying to punch out, she tried an approach shot to the green that caromed off a tree at a 90-degree angle. Her ball ended up in tall grass by a tree adjacent to the 12th fairway, and she kicked her golf bag after seeing where her ball landed. After taking a drop about 20 yards behind where her ball landed, she reached the green with her next shot, but three-putted from 70 feet for a triple bogey. Inkster birdied the first two holes, chipped in for par at No. 4 and took the lead with a birdie on No. 6. She held at least a share of it until the bogey at No. 17. "It's hard trying to win your first tournament, especially on a course like this where it's really tight and narrow and ... it just takes a little bit to get off," said Inkster, who has 31 tour victories. "They will learn from this experience. You can't really tell anybody how to react until they are in it and you have to kind of learn how to play and play with a lead or play tied for the lead." Tour officials moved up Sunday's tee times by two hours and used threesomes instead of twosomes in a successful effort to avoid weather problems.