Cruz Azul were also favoured to beat Morelia but lost 2-1 at home and 4-2 on aggregate, failing to exact revenge after the same rivals eliminated them in the semi-finals of the Clausura championship at the end of last season.
Guadalajara, who finished top of the standings in the round-robin phase of the championship, were held 0-0 at their Omnilife home and went out 2-1 on aggregate in Queretaro's first appearance in the quarter-finals.
The team finishing top of the league table, supposedly an advantage since their quarter-final opponents are the eighth-placed side, has never managed to win the Apertura title since the two-championship format was first played in the 1996/97 season.
Cruz Azul's coach Enrique Meza (pictured), whose side were Apertura runners-up in 2009 in his first season in charge, said he had no intention of quitting despite their wait for a title now standing at 14 years.
"I'm not leaving, even though many [people] want me to go I won't do it. I still have the dream of doing big things [here]," Meza told reporters.
TORRADO OFF
Morelia scored twice in five minutes early in the first half to give Cruz Azul a mountain to climb.
Mexico striker Miguel Sabah put Morelia ahead in the 15th minute after a one-two with midfielder Gerardo Lugo, who added the second five minutes later with a shot from outside the box that beat diving goalkeeper Jesus Corona.
The "Blue Machine" hit the bar in the 32nd minute and pulled a goal back in the 35th when Alejandro Vela netted from Javier Aquino's right cross but they had to play the last 20 minutes without captain Gerardo Torrado.
The Mexico midfielder was sent off for a second booking when he fouled Luis Sandoval.
The match in Guadalajara city was dominated by the Chivas but the closest they came to scoring was a header by Mario de Luna that hit the ground and rose to come back off the bar on the stroke of half-time.
Goalkeeper Liborio Sanchez was the key player for Queretaro, coached by former Paraguay striker Jose Saturnino Cardozo, making a string of fine and often spectacular saves.
