The South Korean continued her superb maiden week on the tour with a final-round 67 to finish 10 under alongside Brittany Lincicome and In Gee Chun.
But it was precocious 19-year-old Baek who held her nerve as extra holes were forced, producing a birdie to edge out Lincicome and Chun when they went back down the par-five 18th on the Ocean Course at Sky72 Golf Club.
Baek headed into the play-off on the back of the poorest round of the trio, her five-under 67 a shot more than Lincicome and compatriot Chun's 66s.
Yet the former had momentum on her side, having produced a super run on the back nine.
After seeing a birdie at four offset by bogeying the sixth, joint-overnight leader Baek caught fire on the way in with five successive gains from 11.
She parred her way in but was quickly on the birdie trail in the play-offs. With Chun hitting her approach into the water, Baek and Lincicome looked set for fours having hit their approaches to five feet.
But while Lincicome missed her birdie putt, Baek kept her cool to add to the three victories she has enjoyed on the Korean tour this year.
Her effort continued a steady improvement over each of the four days, with Baek's scores reading 74, 69, 68 and 67.
Inbee Park finished a stroke behind Lincicome, Baek and Chun after a 67, while Michelle Wie and Catriona Matthew were eight under.