Tee times were moved up Sunday to avoid inclement weather, but the leaders still faced a blustery finish down the stretch. Lincicome birdied the 72nd hole to tie Thompson after a 5-under 68, then got up-and-down again on No. 18 in sudden death for her first LPGA victory since the 2015 ANA Inspiration.
Both players finished the week at 26 under, one shot off the all-time LPGA scoring record relative to par set by Annika Sorenstam in 2001.
While Americans won only two events in 2016, the leaderboard in the Bahamas was painted with red, white and blue. Stacy Lewis finished alone in third place, one shot out of the playoff and undone by a triple bogey on No. 14, while Gerina Piller finished fourth as her search for a maiden victory continues.
Thompson's 3-under 70 included five birdies, but she was unable to birdie any of the final three holes of regulation and missed a 12-foot birdie putt that would have extended the playoff.
While this was the first official LPGA event of the new year, both Lincicome and Thompson already had competitive rounds under their belt after participating in the PGA Tour Champions' Diamond Resorts Invitational earlier this month.