Guillermo Vazquez's men surrendered a two-goal lead to draw 2-2 at home to Leon in their second leg on Saturday, which saw them bow out despite finishing 3-3 on aggregate.
Cruz Azul, who topped the Clausura regular-season standings by four points, earned a 1-1 draw in the opening leg of their quarter-final tie midweek.
And the Mexican giants appeared to be on track for the final four after taking a two-goal lead thanks to Mariano Pavone and Mauro Formica at the Estadio Azul.
The home side opened the scoring in the 12th minute when Formica's effort was rebounded into the net by team-mate Pavone - his third goal in as many games.
Cruz Azul doubled their lead nine minutes later through Formica, who fired his low strike past helpless goalkeeper William Yarbrough.
Just as Cruz Azul seemed in control, Leon sent shockwaves through the stadium when former Wigan striker Mauro Boselli pulled a goal back five minutes from the half-time interval.
Leon's stunning comeback was complete on the hour-mark thanks to Luis Montes, who weaved his way past two defenders before finding the bottom right-hand corner.
Leon will face Toluca in the semi-finals after they progressed 3-1 on aggregate at the expense of Tijuana on Sunday.
The opening leg ended scoreless but two goals in the second half from Toluca duo Miguel Ponce and Edgar Milciades lifted the home side to victory.
Joining Toluca in the semis are Santos Laguna, who recorded a late 3-1 win over America at the Estadio Nuevo Corona on Saturday.
Two goals in the final seven minutes from Ribair Rodriguez and Andres Renteria lifted Santos Laguna to success on away goals after the last-eight tie ended 6-6 on aggregate.
America had triumphed 5-3 on home soil in the first leg but they were no match for Santos Laguna on the road, despite netting a 90th-minute goal through Rubens Sambueza.
Next up for Santos Laguna are Pachuca following their 3-1 triumph at Pumas UNAM on Sunday.
Enner Valencia was the hero, bagging a hat-trick as Pachuca advanced 4-2 on aggregate.
