Lucas da Silva opened the scoring for the Bravos in the 30th minute, when he finished off a corner kick to make it 0-1 for the visitors.
Chivas pushed for a tying goal and Carlos Fierro nearly found one on a pair of occasions, but he first sent his shot wide and then was denied by a great save by Cirilo Saucedo.
Then, in the 49th minute, Juárez made it 0-2. Da Silva received a through ball and shot past the onrushing Jiménez to shock the hosts.
Chivas adjusted their tactics after conceding a second, and they soon were able to reduce the deficit. In the 56th minute, Fierro sent a low cross into the box for Rodolfo Pizarro. The substitute finished it off to make it 1-2 and put Chivas back into the game.
The equalizer then came from the penalty spot, with Ángel Zaldívar putting the spot kick just out of the reach of Saucedo to make it 2-2 in the 68th minute.
With a penalty shootout looming to separate the sides, Javier López sent a shot from outside the box into the back of the net to give Chivas a dramatic 3-2 victory.
With the 3-2 win, Chivas advances to the semifinals while Juárez is eliminated.