Chivas slipped to 15th position in the Mexican Apertura championship after a 4-2 loss to Puebla on Sunday which prompted the dismissal of coach Benjamin Galindo.
Morelia improved to first in the league after Friday's 2-1 victory over Atlas, while Veracruz dropped to second after a 0-0 draw against Queretaro on Saturday.
In other games this weekend, Santos Laguna defeated Tigres 3-0, Cruz Azul overcame Atlante 1-0, America won 1-0 against Pachuca, Toluca thrashed Chiapas 4-0, Monterrey snatched a 2-1 victory over Tijuana and Pumas tied 1-1 with Leon.
An own goal from Kristian Alvarez in the 64th minute and a Matias Alustiza strike eight minutes from time helped Puebla to its first win of the season.
Antonio Gallardo handed Chivas the lead with a curling shot from 25 yards (meters) in the 10th, but a defensive lapse from a corner left Jesus Chavez alone to head in two minutes later for Puebla.
Chivas again went in front in the 36th through a close-range header from Rafa Marquez Lugo, but Alfredo Moreno's cross-cum-shot found its way into the bottom corner of the net in first half injury time to bring the scores level.
The result means Chivas, which has 11 league titles and is Mexico's most popular club along with America, is already under pressure with only one win in its last 11 league games stretching back to last season.
Galindo was fired in the immediate aftermath of the game. Galindo took over from Dutch coach John van't Schip in January.
Morelia took the lead in the 71st when Rodrigo Salinas controlled a long through ball and slid the ball past goalkeeper Miguel Pinto.
Aldo Leao Ramirez drove the ball in at Pinto's near post for Morelia's second in the 81st.
