The 25-year-old Thai player is the sixth first-time winner on tour this year. Her previous best finish in 120 starts was seventh at the 2014 Kingsmill Championship.
Suwannapura picked up three strokes over her final two holes, making eagle on the par-5 17th and closing with a birdie on the par-5 18th at Highland Meadows to finish at 14-under 270.
In the playoff, Suwannapura converted a short birdie putt after Lincicome hit her second shot into a water hazard and scrambled for par.
Lincicome shot 67. She had a chance to win in regulation, but her birdie putt from about 10 feet did a nearly 360-degree turn around the edge of the cup and stayed out. Next up for the big-hitting Lincicome: a start against the men at the PGA Tour's Barbasol Championship.
Third-round leader Brooke Henderson led by two shots after six holes, but struggled the rest of the way. Back-to-back bogeys on the 14th and 15th holes dropped her out of the lead. The 20-year-old Canadian finished with a 2-under 69, one shot out of the playoff.
Princeton's Emma Talley shot a final round 68 to finish tied for 5th at 11 under. It's her second top-five finish in as many weeks. Talley is now 35th on the LPGA Tour money list after earning $52,301 at this week's tournament.
