Puebla picked up only their second win of the tournament and their first under coach Mario Carillo after Guadalajara coach Efrain Flores controversially decided to field a reserve team.
Guadalajara face Brazil's Internacional in a Copa Sudamericana tie on Wednesday.
Luis Miguel Noriega and Sergio Rosas put Puebla 2-0 ahead by halftime while the Chivas had Patricio Araujo sent off for a bad tackle on Cesareo Victorino.
Sergio Santana pulled one back in the last minute for the Chivas, who dropped to fifth in Group Two with 22 points from 16 games.
The 18 teams play each other once in the competition but are divided into three groups, with the top two in each qualifying for the quarter-final.
The two teams with the best record of the remainder, regardless of group, also go through, a criteria which now represents Guadalajara's only realistic hope of qualifying.
America, the country's richest club, kept their faint hopes alive by beating Monterrey 1-0 with an early goal from Argentine Alfredo Moreno.
Although bottom of Group Two with 21 points, America could still sneak through as one of the best of the rest.
Monterrey, under former Mexico coach Ricardo La Volpe, have 16 points in Group One and are mathematically eliminated.
