The win was her third career LPGA Tour victory.
The four participants each scored birdies down the stretch to finish 72 holes on the Highland Meadows course tied at 14-under-par 270.
Choi, who led after each of the three previous rounds, sank a birdie on the 18th in regulation to finish with a 71 and join the playoff.
Christina Kim (70) missed a chance to win the tournament on the 18th when her 10-foot birdie putt couldn't find the cup.
In-Kyung Kim (64) and Song-Hee Kim (66) each had sizzling rounds Sunday to push their way to the top and force the four-way playoff.