Lewis was a two-stroke winner over Choi Na-yeon and Park Hee-young for her second major title (2011 Kraft Nabisco Championship) and that keeps her in the No. 2 spot in the world women's golf ranking.
Choi remains fourth in the rankings while Park moves up six places to 15th. Suzann Pettersen, the only other Top 10 player to finish in the upper tier last week at St. Andrews, is still third.
Shin was the defending Women's British Open champion but tied for 36th this year and slips from eighth to 10th in the rankings. Catriona Matthew, who tied for 11th Sunday, goes from 10th to eighth.
No. 1-ranked Inbee Park was seeking a fourth major tournament title of this year but wound up tied for 42nd after a final round of 6-over 78. She'll have another shot at a fourth major -- women's golf has five major tournaments -- in September at the Evian Championship in France. No player has won more than three in a calendar year.
The world women's golf Top 10 with player's name, home country, ranking point average and finish at the Women's British Open:
1. Inbee Park, South Korea, 12.91, tie for 42nd
2. Stacy Lewis, United States, 9.74, first
3. Suzann Pettersen, Norway, 8.26, tie for fourth
4. Choi Na-yeon, South Korea, 7.94, tie for second
5. Ryu So-yeon, South Korea, 7.16, tie for 17th
6. Karrie Webb, Australia, 6.19, missed cut
7. Feng Shanshan, China, 5.97, tie for 25th
8. Catriona Matthew, Scotland, 5.59, tie for 11th
9. I.K. Kim, South Korea, 5.56, tie for 47th
10. Jiyai Shin, South Korea, 5.56, tie for 36th