The 24-year-old Meena Lee closed with a 7-under 65 to match the 20-year-old Seon Hwa Lee (71) at 14-under 202 -- a stroke ahead of the hometown favorite Wie (66) -- and won with a 6-foot birdie putt on the third extra hole.
Meena Lee earned $165,000. She won the Canadian Women's Open last year.
The win completed a South Korean sweep of Hawaii to start the season. Joo Mi Kim won the season-opening SBS Open last week at Turtle Bay.
Seon Hwa Lee, also from South Korea, missed a 10-foot birdie putt that curled to the left, leaving the door open for her opponent. She was trying to win her first LPGA Tour title in her third career start.
Seon Hwa Lee began the day with a two-stroke lead over Natalie Gulbis at 13 under. Seon Hwa Lee earned a spot on the tour by leading the Futures Tour money list last year after winning three times on the Korea LPGA.
A flurry of birdies late in the day, with several players jostling for the lead, made for an exciting finish at Ko Olina Golf Club.
Wie had seven birdies and a costly bogey to close with her 66 and finish third at 13-under 203. She earned $72,875 for her first paycheck in four pro starts. The 16-year-old star was disqualified from the LPGA Tour's Samsung World Championship in October in her pro debut, and missed the cut in two men's events.
Meena Lee began the day birdie-eagle and ended the day with a birdie.
Seon Hwa Lee had a chance to win in regulation, missing a 12-foot birdie putt on No. 18.
The Lees both parred the first two playoff holes, Nos. 18 and 16, with Seon Hwa Lee missing a 20-foot birdie putt that would have ended it on the first extra hole.
Meena Lee holed a clutch 8-footer to save par and send it to a third playoff hole.
Mexico's Lorena Ochoa, who lost a playoff in the season-opening SBS Open last week, closed with a 70 to tie for fourth at 11 under with Nicole Castrale (69), rookie Julieta Granada (71) and Natalie Gulbis (72). Karin Sjodin (68) was another stroke back, with Cristie Kerr (69) and Lindsey Wright (70) at 9 under.
Wie moved into contention early by birdieing four of her first six holes in a front-nine 32 that left her two strokes behind Seon Hwa Lee.
Wie was playing in front of a huge hometown gallery, which was packed 10 deep to watch her first tee shot of the day and cheered every swing. She was paired with 17-year-old Morgan Pressel, the youngest player on the tour, and 49-year-old Sherri Turner, the oldest player entered in the event.
Pressel, the U.S. Amateur champion and U.S. Women's Open runner-up, was in tears after her 71, giving her a three-day total of 8-under 208. She tied for 11th with 2005 rookie of the year Paula Creamer (67), Jeong Jang (68), Angela Stanford (67), Sophie Gustafson (69), Sakura Yokomine (70), Wendy Ward (72) and Aree Song (72).
Pressel made the turn at 2-under 34 to put her at 9 under, but couldn't get any closer.