Emmanuel Cerda opened the scoring for the visitors with a goal after 35 minutes.
Lucas Lobos scored a second for Monterrey after 77 minutes to move his team a point behind Santos Laguna and Morelia in the league standings.
Emanuel Villa turned from hero to villain for Cruz Azul as he scored but was also sent off in the 1-1 draw at Puebla.
Villa opened the scoring after 10 minutes before DaMarcus Beasley levelled things after 56.
But Villa was then shown a red card with five minutes of the game remaining.
Cruz Azul were able to hang on with 10 men to ensure they took one point from the game which puts them 10th in the table, while Puebla are in the bottom three.