Lewis, 28, finished at 8-under 280 after a final round of even-par 72. She finished two strokes ahead of South Koreans Na Yeon Choi and Hee Young Park. American Morgan Pressel, who held the lead at the 54-hole mark, tied for fourth with Norway's Suzann Pettersen after a final-round 76.
It was the second major championship for Lewis, who previously won the 2011 Kraft Nabisco Championship. No American had won a major in the 10 previous ones, the longest such streak in women's golf. All 10 of those majors had been won by players from Asian countries, including the last three by Inbee Park of South Korea.
'I felt so comfortable all week, and I just hung in there and hung in there and hung in there,' said Lewis, ranked No. 2 in the world. 'And to finish the way I did was just awesome.'
Inbee Park, seeking a fourth consecutive major, was never in contention. She shot a final-round 78 and tied for 42nd.