Inkster, 51, birdied three of the final five holes at the Guadalajara Country Club to shoot a 3-under 69 and was tied for first place with Anna Nordqvist at 8-under 136.
Nordqvist posted a 65, the low round of the tournament.
Beth Daniel currently holds the record as the oldest LPGA Tour winner. Inkster is almost five years older than Daniel was when she established the record in 2003.
Suzann Pettersen, who was tied for the lead with Inkster after the opening round, shared third place Friday at 137 with Catriona Matthew and Meena Lee. Defending champion I.K. Kim was alone in sixth at 138.
Inkster was bothered by a sore right elbow during the first round and received a cortisone shot.
She again felt discomfort during the second round and was only 1-under through 13 holes before holing birdie putts at the 14th, 15th and 18th.
2014: The Year in Music [PHOTOS]