In the other semi-final, a goalkeeping error by Alejandro Palacios allowed striker Omar Arellano to notch an 89th-minute equaliser and give Guadalajara a 1-1 home draw against Pumas UNAM.
Defender Efrain Velarde had headed Pumas into the lead after 51 minutes in a match in which both teams played the second half with 10 men.
Guadalajara's Hector Reynoso was shown the red card after half an hour and David Cabrera of Pumas was sent off for a second booking on the stroke of half-time.
At the Estadio Azul, midfielder Gimenez put Cruz Azul ahead just before the half hour when compatriot Federico Vilar in the Morelia goal could not hold his stinging shot.
Striker Villa added the second on the stroke of half-time for the "Blue Machine", who are looking for their first title since 1997.
The second leg matches are on Sunday.
Toluca, Clausura champions last year, said on Thursday they had sacked coach Sergio Lugo after his team's failure to qualify for the eight-team knockout phase.
Mexico City giants America, on the other hand, ratified Chilean coach Carlos Reinoso as coach despite the team's quarter-final elimination last weekend.
Tigres UANL, also knocked out in the quarter-finals after finishing top of the overall standings, said they would retain all five foreign players on their squad, including Chile striker Hector Mancilla, for next season.
