Kim, Ariya Jutanugarn and Sun Young Yoo couldn't be separated on 14-under after four rounds of play, but it was Kim who produced the goods when it really mattered, registering a birdie on the first play-off hole to take the win.
The South Korean missed the cut at last week's season-opening Coates Golf Championship, her first LPGA tour event, but turned things around this week as she shot a final round 68 to boost herself into the share of the lead.
Kim was joined at the top of the leaderboard by compatriot Yoo who had enjoyed a share of the lead heading into the final round, and Thailand's Jutanugarn who carded a final round 69.
However, Kim soon separated herself from the rest, sinking an 8-foot birdie putt on the first play-off hole.
Brittany Lincicome came home in fourth on 13-under, with Inbee Park and Danielle Kang a further shot back.
Park had looked set to take the world number one ranking off Lydia Ko after just a week, but her final round 72 saw her drop down the field and finish just one place above Ko who was tied for seventh on 11-under, not a large enough margin to see a change at the top of the rankings.