MEXICO, 16 Nov 2014 (AFP) - The 30-year-old American has one of the longest winless droughts on the tour -- her last victory came in 2005 at the Tournament of Champions.
Kim, who began the day just one shot ahead of Paula Creamer, finished 54 holes at 14-under-par 202.
China's Feng Shanshan also shot a 68 at Club de Golf Mexico, which vaulted her into sole possession of second place at nine-under 207.
South Korea's Ryu So-Yeon (69), Pornanong Phatlum (71) of Thailand and Spain's Azahara Munoz (71) are all tied for third at eight under.
World number one Park In-Bee got into contention with a three-under 69 and she is alone in sixth at seven-under 209.
Defending champion Lexi Thompson fired a two-under 70, her third consecutive round in the 70s, and she is tied for 10th at four-under 212.
Scores on Saturday after the third round of the LPGA Lorena Ochoa Invitational (USA unless noted, par 72):
202 - Christina Kim 65-69-68
207 - Shanshan Feng (CHN) 72-67-68
208 - Pornanong Phatlum (THA) 69-68-71, So Yeon Ryu (KOR) 70-69-69, Azahara Munoz (ESP) 66-71-71
209 - Inbee Park (KOR) 70-70-69, Brittany Lincicome 70-71-69
211 - Paula Creamer 70-65-76, Lydia Ko (NZL) 68-69-74
212 - Suzann Pettersen (NOR) 71-66-75, Lexi Thompson 70-72-70
213 - Michelle Wie 73-69-71, Julieta Granada (PAR) 71-71-71, Jenny Shin (KOR) 71-71-71, Lizette Salas 69-72-72
214 - Karine Icher (FRA) 70-73-71, Gerina Piller 69-70-75