Lang's short putt for birdie on the 18th hole handed her a triumph over three playoff opponents -- Hee Kyung Seo, Chella Choi and third-round leader Inbee Park.
After Choi was eliminated on the first playoff hole and Park exited after the second extra hole, it came down to Lang and Seo on the third.
Lang's decisive putt atoned for a missed try on the same green that would have handed her a regulation victory. She shot a 4-under 67 to join Choi (63), Park (69) and Seo (67) at 16-under 268.
Sharing fifth place at minus-15 were Stacy Lewis and So Yeon Ryu, both of whom fired 7-under 64s.