Argentine Villa struck in the 90th minute for Cruz Azul, who had already secured their berth in the last eight, when he took a right cross from Rogelio Chavez, rounded defender Edgar Mejia and keeper Luis Michel and slotted home.
Guadalajara, who were on top for most of the match, had Edgar Solis sent off for a violent foul with eight minutes remaining and lost the initiative.
Puebla and San Luis took the last two places in the knockout phase despite losing their last matches of the qualifying phase.
Puebla lost 2-0 at home to Group One winners Toluca, the best team of the season so far, while San Luis were crushed 4-0 away to promoted Queretaro, who did not qualify for the last eight.
The line-up for next weekend's quarter-final first leg matches is: Toluca v San Luis, Cruz Azul v Puebla, Morelia v Santos Laguna and America v Monterrey.
Title holders Pumas UNAM will not be defending their crown after a poor championship in which they finished bottom of Group Three with four wins and 17 points in 17 matches.
Only Indios from Ciudad Juarez, who held Pumas 1-1 in Mexico City on Sunday, fared worse, ending the tournament bottom of Group One with no wins and six points.
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