Francisco Ramirez was named head coach on Thursday, replacing Omar Arellano, who left after only three matches.
The Guadalajara hero was goalkeeper Luis Michel, who made three key saves in the second half.
The game's only goal came in the 68th minute when Sergio Ponce scored on a header off Alberto Medina's cross.
The win moved Chivas into second in Group Two with 19 points. America dropped to fourth with 18 points. Three games remain in the Torneo Clausura's second stage.
America had changed coaches in February, naming U-20 national team coach Jesus Ramirez as its fifth coach in a year after Argentine Ramon Diaz was fired.
Group 1 -Pachuca 27 points; Puebla 24; Monterrey 23; Santos 18; Indios 14; Atlante 13.
Group 2 -UNAM 24; Guadalajara 19; UAG 18; America, Morelia 17; Cruz Azul 12.
Group 3 -Toluca 29; Atlas 20; Chiapas 19; San Luis 16; Tigres, Necaxa 12.