Gillespie, a Canadian, is seeking his third career win and first since the 2003 Corona Ixtapa Classic.
He began the round five shots off Richard Gilkey's lead, but rallied to reach 15-under 201 with a round that included an eagle, five birdies and just one bogey.
Surprising rookie Spencer Levin had the lead Saturday until an unfortunate closing double-bogey at the par-4 18th. He shot a 3-under 69 and was one shot back at 14-under 202.
Gilkey, the overnight leader, stumbled to a 1-over 73 and was tied for third place with Mike Mezei (67) at 13-under 203. Bret Guetz (68) was another shot further back at 204.
This is the last of four consecutive Canadian Tour events in Mexico before the circuit shifts north to Canada for the summer swing.