Guadalajara qualify for play-offs
Winger Omar Arellano scored the only goal in the 36th minute at the Jalisco when he shot inside the far post from a narrow angle after tricking keeper Guillermo Ochoa into thinking he was going for the near post.
America had Chile forward Jean Beausejour sent off in the final minute for a kick at Chivas substitute Xavier Baez that sparked fighting among players.
"To win the clasico is always indescribable," Guadalajara's Mexico goalkeeper Luis Michel told reporters.
Guadalajara lead Group One with 31 points, 11 ahead of second-placed Toluca, who crushed Estudiantes UAG 5-0, and 13 in front of Queretaro with four matches to go.
The top two teams in each of the three groups qualify for the play-offs.
Title holders Monterrey, who won the Apertura in December, lead Group Two nine points ahead of Morelia and 10 in front of Pachuca. America are fourth 12 points adrift of Monterrey but only three behind Morelia.
Group Three is headed by Santos Laguna, beaten 3-0 at home by Chiapas. They have a one-point lead over Apertura runners-up Cruz Azul with Pumas UNAM third two points further back.
Santos Laguna's Carlos Morales took a bad knock to the head after he collided with Christian Armas's knee and was put into an induced coma to reduce the inflammation in his brain, El Universal's sports website reported.
Morales was not knocked unconscious and he played on until half time after receiving pitch-side treatment. However, at the interval he was taken to hospital.