America had lost 3-0 to arch-rivals Guadalajara, the Chivas, last weekend but two goals from Angel Reyna helped them to a potentially crucial win over the Tecos, the western city's university team, to retain second place in Group Two.
Atlante lead the group with 23 points after Saturday's 1-1 draw with relegated Necaxa. America have 22 with Toluca and Atlas on 20, with two matches to go in the qualifying, round-robin phase.
The top two teams in each of the three groups, plus the next two best-placed teams in the overall standings, qualify for the quarter-finals.
Group Three leaders Pumas UNAM, who qualified the previous weekend with three matches to spare, notched their ninth win when they beat Queretaro 3-0 at the Olimpico on Sunday.
Former Mexico striker Francisco Palencia scored twice in the opening 18 minutes, his first with a diving header, and laid on the third for Paraguayan Dante Lopez.
Pumas have 32 points with two matches to go, four more than Morelia, who have also qualified after a 1-1 draw at Monterrey on Saturday, and eight ahead of Cruz Azul, who lost 2-0 at Puebla.
Group One leaders Tigres UANL secured their berth in the last eight with a 1-0 win at Chiapas. They are five points ahead of Guadalajara with title holders Monterrey third on 22.
