America, one of Mexico's most popular clubs who had not made it to the play-offs for two years, are among six teams who have secured their berths in the last eight with one match to go in the round-robin phase.
The top two teams in the three groups and the two highest in the overall standings go through to the quarter-finals.
"We completed the first objective which was to qualify, we did it winning which is also important," Montenegro, who headed home Pavel Pardo's cross from the left in the 16th minute, told Televisa.
Group One leaders Toluca, who qualified a week ago, crushed Pachuca 3-0 with two goals from Chilean Hector Mancilla.
Guadalajara, who sacked coach Raul Arias in midweek after three successive defeats, kept their hopes alive of taking second place in the group with a 4-1 win over Ricardo La Volpe's Atlas, whose chances have evaporated.
Morelia, who drew 0-0 with title holders Pumas UNAM, lead Group Two ahead of America and Monterrey, who although they are third have made sure of taking one of the places available from the overall standings.
Pumas, who made a very poor start to the season, are bottom of Group Three and out of the running.
Group Three leaders Cruz Azul booked their place with a 4-0 rout of Puebla, Argentine striker Emanuel Villa scoring twice to take his championship leading tally to 16, four more than second-placed Mancilla.
Santos Laguna also qualified from second place despite a 4-2 defeat by San Luis after third-placed Atlante, the CONCACAF champions, crashed to a 4-0 loss against Tigres UANL with two players sent off.
Argentine striker Alfredo Moreno scored a hat-trick for San Luis.
