After Wednesday's 1-0 first-leg loss to Pumas UNAM, Paolo Goltz levelled the aggregate score at 1-1 with a 75th-minute header in the return match at the Estadio Azteca on Saturday.
America progressed to the final four due to their superior standing in the regular-season Liga MX table.
Antonio Mohamed's America topped the table, while Pumas were eighth.
Pumas, who went on an eight-match unbeaten run to reach the play-offs, took a slender one-goal lead into the weekend's second leg thanks to Eduardo Herrera.
The Mexican striker headed the ball into the bottom corner of the net 11 minutes from time at the Estadio Olimpico de Universitario in Coyoacan.
But Pumas were hauled back at a similar stage in the return fixture, Goltz using his head from a corner with 15 minutes left on the clock to send America through to the semis.
Tigres also benefited from their position in the standings after drawing 2-2 with Pachuca on aggregate on Saturday.
The scores were tied over two legs after Hugo Ayala's 38th-minute fortuitous rebound cancelled out Ariel Nahuelpan's opener and earned hosts Tigres a 1-1 draw in San Nicolas de los Garza.
And Tigres' runner-up finish in the regular season ensured their passage into the next round.
Atlas crashed out of the Apertura play-offs at the first hurdle, losing 2-1 on aggregate against Monterrey.
Tomas Boy's Atlas - third during the regular season - won the opening leg 1-0 away from home on Thursday but they could not repeat that feat on Sunday, as Monterrey triumphed 2-0.
Meanwhile, Toluca's fourth-placed finish saw them move into the semis following their 2-2 aggregate stalemate with Chiapas on Sunday.
