Beasley ends Pumas' unbeaten record
Guadalajara, who beat Monterrey 2-1 at home on Saturday, remained top of the standings two points ahead of Pumas and Cruz Azul, 2-1 winners over promoted Tijuana.
The America and Atlas players took the field at the Azteca carrying a banner saying "Together for a Mexico without violence" in reference to drugs-related violence that has swept across Mexico.
Saturday's match between Santos Laguna and Morelia in Torreon was suspended in the 40th minute with the score 0-0 when a gunfight broke out outside the stadium in the northern city when three vehicles with armed men failed to stop at a military checkpoint.
With Argentine Daniel Montenegro commanding in the America midfield, Benitez scored three goals in the final 20 minutes.
Winger Angel Reyna and Uruguayan Vicente Sanchez had given America a 2-1 lead following Honduran Georgie Welcome's early opener for Atlas.
Brazilian Flavio Santos pulled another goal back in the 81st minute.
Puebla went two up against Pumas in the opening half hour at the Cuauhtemoc stadium with a free-kick by Alan Zamora and a header from U.S. midfielder DaMarcus Beasley from Aldo Polo's right cross.
Pumas, who played with 10 men for 53 minutes after midfielder David Cabrera was sent off following a second booking, pulled back a late goal with a free-kick from Javier Cortes.