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, with 28 points from 15 matches, have secured a place in the knockout phase of the Apertura championship with two games to spare. The top eight go through after the 17 matches of the league format.
Santos Laguna, who drew 1-1 at home with America, are four points behind in second place with a match in hand.
Title holders Pumas UNAM are also on 24 points after they beat Atlante 1-0 at home in Mexico City. Tigres are six points adrift of Guadalajara in sixth place.
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 would have lost but for a fine one-handed penalty save by goalkeeper Armando Navarrete after a handball by their Colombian captain Aquivaldo Mosquera.
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.
