After Kim squandered a chance to win in regulation when she missed a one-foot par putt on the final hole, Yoo went on to capture the first women's major of the year when she birdied the same hole to start the play-off at Mission Hills Country Club in Rancho Mirage, California.
"I'm speechless right now. I played pretty solid today," Yoo, who matched Kim with a final round of three-under-par 69, said in a TV interview by the green. "I was hoping today for some luck. Looks like I got lucky. I'm very happy."
Yoo then joined her caddie for a running jump into Poppie's Pond for the winner's traditional splash in the water that surrounds the 18th green.
The jubilation was in marked contrast to the stunned reaction by Kim after her tap-in par putt on the 72nd hole caught the right edge, spun around and headed back to her.
After sinking the bogey putt she covered her ears with her hands as she walked off and looked skyward in dismay before heading back to the 18th tee to start the play-off with the duo tied at nine-under-par 279 after 72 holes.
Yoo knocked her tee shot in the fairway, while a still wobbly Kim drove her ball deep into the left rough.
Kim's third shot settled on the edge of the green about 30 feet from the cup, while Yoo set up her winning birdie putt with a laser-like approach shot.
Five-time Major winner Yani Tseng of Taiwan (73), who began the day tied for the lead, narrowly missed joining the play-off when she missed a long, curling birdie putt at the 18th to finish one shot back of the leaders.
Tied for fourth at 281 were 2011 winner Stacy Lewis (66), Koreans Amy Yang (69) and Seo Hee-kyung, and unheralded Swede Karin Sjodin (74), who was co-leader after three rounds.
Sjodin had a three-shot lead early in the round after an eagle at the second hole, while Seo surged to a three-shot edge in the back nine before stumbling.