Lewis finished at 8-under-par 280 on the Old Course at St. Andrews, capturing her second major title and the first for any American in an LPGA Tour major since the 2011 Kraft Nabisco, which she also won.
With the triumph, she joined Sherri Steinhauer as the only American women to win the British event since it became a major tournament in 2001.
Sharing second place at 6-under 282 were second-round leader Na Yeon Choi and Hee Young Park, both of whom shot 1-over 73 in the final round.
Taking sixth place one shot further back was Lizette Salas (73).
Inbee Park, who was seeking her fourth major title of the year, ended at 6-over 294.