Chivas (Goats) midfielder Alberto Medina (pictured) surprised the home faithful almost as much as Tigres' (Tigers) when he unleashed a shot from outside the box past Enrique Palos for the only goal six minutes after half-time.
Tigres midfielder Manuel Viniegra had been sent off after 25 minutes for a nasty foul on Marco Fabien de la Mora, leaving his team with an even tougher task in front of a crowd of 30,000 baying for blood after Chivas scored eight goals in their previous two games.
The visiting side's Argentine playmaker Lucas Lobos almost equalised at the death but failed to get high enough to substitute Edgar Pacheco's cross to bring it down into the goal and his effort was just wide.
Guadalajara's arch-rivals America, beaten 3-1 by Chivas at the Azteca on Sunday, continue to languish near the bottom of the table with little chance of a quarter-final berth after their draw at Santos.
America were without Mexico forward Angel Reyna, who was suspended indefinitely by the club for saying publicly his team had a "watery captain and a plastic defence" after their weekend defeat by Guadalajara.
