The American fired four straight birdies on her way to an 11-under 133 after 36 holes at the Guadalajara Country Club.
Stanford is looking to win the $1 million tournament for a second time, having claimed victory at the inaugural event in 2008.
South Korea's Inbee Park ended the second round on 135 with another American Cristie Kerr a further shot back in third place on the leaderboard.
Stacy Lewis, the world number two who is looking to secure the LPGA Player of the Year points race over the next week, was tied for fourth at seven-under with South Korean So Yeon Ryu and Candie Kung of Taiwan.
American Lewis, who picked up her fourth title of the season last week in Japan, holds a 58-point lead over Park with just the Lorena Ochoa Invitational and next week's season-ending LPGA Titleholders event in Florida remaining.
South Korean I.K. Kim and France's Karine Icher were another stroke adrift.
Michelle Wie, who held the overnight lead with Stanford and Kung, dropped down to 12th after shooting a 75 - in stark contrast to her 66 a day previously.