Taking a back pass from Tatiana Ariza, Montoya drilled home a shot from just outside the penalty area that rang off the crossbar in the 82nd minute to deny Mexico a first World Cup win.
Mexico was the better team dominating possession, grabbing the early lead on a brilliant 36th minute strike from midfielder Veronica Perez.
El Tri thought it had pulled out a miracle finish in injury time when striker Charlyn Corral's shot rolled across the goal line only to have it waved off when teammate Stephany Mayor was called for a foul on Colombia's Angela Clavijo.
Ranked 26th in the world, Mexico will play England in its next game, while number 28 Colombia will face France.
