Santos, who had been held 0-0 at home in the first leg of their quarter-final, will meet Cruz Azul, who went through 4-3 on aggregate despite losing 1-0 away to Morelia.
In the other semi-final, Monterrey face 10 times champions America after they both qualified on Saturday.
Striker Omar Bravo gave Atlas the lead with five minutes gone when the referee ruled his shot had crossed the line after Facundo Erpen's header had been saved by Santos goalkeeper Oswaldo Sanchez.
'The Warriors' equalised in the 15th when Andres Renteria slotted home after Atlas goalkeeper Miguel Pintos failed to hold a shot from Quintero.
In the 25th minute, Pinto was sent off for handling a scoring chance outside his box after being wrongfooted by a headed back pass from Erpen.
Quintero put Santos, Clausura champions a year ago, ahead in the 62nd from Renteria's cross and secured the win in added time on a solo breakaway.
Atlas coach Tomas Boy did not take kindly to Quintero's celebrations in front of the home side's bench and almost came to blows with Santos coach Pedro Caixinha.
Cruz Azul's run of six victories came to an end but they qualified on the back of their 4-2 home win over Morelia in the first leg on Thursday. They conceded a goal on the stroke of halftime to Rodrigo Salinas at the Morelos stadium but held on for the aggregate win.
At the Azteca on Saturday, striker Christian Benitez scored twice as America beat Pumas UNAM 2-1 in a Mexico City derby for a 3-1 aggregate victory.
Robin Ramirez scored in the 21st minute for Pumas to level the score on aggregate before Benitez, top scorer in the championship with 14 goals, equalised in the 56th minute and hit the winner in the fourth minute of added time.
CONCACAF Champions League winners Monterrey drew 1-1 at Tigres UANL and went through 2-1 on aggregate.
Tigres were the latest victims of the so-called "curse of the superleaders", the team finishing top of the league phase of the championship from which the top eight go through to the knockout rounds.
In the 34 championships since the introduction of two per season in 1996, the leaders of the league phase have only prevailed six times.
- Sports & Recreation
- Cruz Azul
- Facundo Erpen