The 29-year-old South Korean player birdied the par-5 16th and par-4 17th and parred the par-4 18th to finish at 21-under 267 at Blythefield Country Club.
Two strokes behind Anna Nordqvist and Lee-Anne Pace entering the round, Ryu had six birdies and bogey in the final round.
Caroline Masson was second after a 68. Lydia Ko shot a 67 to finish third at 18 under.
Nordqvist and Pace each shot 73 — after each had a 64 on Saturday — to tie for fourth at 17 under with Jacqui Concolino (66), Azahara Munoz (68) and Angela Stanford (70).
U.S. Women's Open winner Ariya Jutanugarn shot a tournament-record 62. She birdied five of the first seven holes, eagled No. 8 and added three more birdies to finish 12th at 15 under.