Holders Toluca, however, are in danger of failing to make the cut.
The three qualifiers joined Monterrey and Cruz Azul, group winners who had already booked their places, in the eight-team play-offs.
Chiapas, who beat Atlas 2-1 with Colombia's Jackson Martinez scoring the winner, are on the verge of joining them provided they do not lose next weekend. They are second in Group Three, two points ahead of Pumas UNAM.
The top two in each group plus the next two best-placed teams qualify.
Through so far are Monterrey and Santos from Group One, America and San Luis from Group Two and runaway Group Three leaders Cruz Azul who have the most points overall.
America, one of Mexico's most popular and successful teams, beat Atlante 1-0 away with a goal by former Mexico forward Matias Vuoso to climb into first place in Group Two, one point ahead of San Luis.
They could have scored a second goal but former Mexico midfielder Pavel Pardo missed a late penalty.
America's great rivals Guadalajara, runners-up in the South American Libertadores Cup in July, must win their last match next weekend and hope other results go their way to finish third in Group One and advance as one of the next two best-placed teams.
Guadalajara were held 0-0 at home by Cruz Azul this weekend.
Toluca, who won the Clausura championship in the second half of last season, are fourth in Group Two and a win next weekend would put them on 24 points which might be enough to qualify.
CONCACAF Champions League holders Pachuca, who will take part in the Club World Cup in Abu Dhabi next month, beat Queretaro 2-0 with two goals from Argentine-born Croatian Dario Cvitanich.
They are third in Group Two with 22 points.
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