Stanford, winner of this year's HSBC Championship, concluded 36 holes at the Guadalajara Country Club with an 11-under total of 133. One of her five LPGA Tour victories came in this event in 2008.
Inbee Park was alone in second at 135 after firing a 68. Cristie Kerr was another shot back.
Kung was tied for fourth at 137 with Stacy Lewis and So Yeon Ryu. Lewis is coming off a win last week in Japan.
Wie dropped to 12th place at 141 after shooting a 75. Tournament host Lorena Ochoa was tied for 19th in the 36-player field.
2014: The Year in Music [PHOTOS]