Stanford dropped a 3-foot putt on the third playoff hole while Jenny Shin's par try lipped out. Shanshan Feng and Choi No-yeon were in the playoff but had been eliminated earlier.
They all completed 72 holes at 10-under 278, one stroke better than Yani Tseng and three ahead of Ai Miyazato and Kim In-kyung.
It was the fifth LPGA title for Stanford, but first since 2009.
And she had to wait for it Sunday, too. She was down one stroke going into the 72nd hole when thunderstorms hit. Play was suspended for about 2 hours.
Shin was leading Stanford by one stroke at that point but hit her drive into the woods when play resumed and ended up with a double bogey 6. Stanford missed a putt of about 5 feet to win the tournament and settled into the four-way playoff.
Feng was eliminated on the first playoff hole with the other three players all managed par. Choi dropped out on the second hole, again after Shin and Stanford had pars. That set up the third playoff hole, which Stanford won with another par.
Stanford shot 1-under 71 after four birdies and three bogeys in the final round. Choi opened Sunday with a bogey but finished with a 4-under 68.
Feng was bogey-free until the 18th hole en route to a final round of 3-under while Shin, in addition to the double bogey on the final hole had two bogeys and five birdies in the fourth round.