The Colombian Primera A side travelled to Brazil with work to do, after the Serie A side scored two away goals in the first leg in Medellin.
But Juan Carlos Osorio's men ensured themselves of progression with a 1-0 victory, Daniel Bocanegra's second-half goal at the Estadio Manoel Barradas enough for the Colombians.
Defender Alexis Henriquez's header from a corner came back off the crossbar, and Bocanegra was on hand to tap home the decisive goal in the 70th minute.
Atletico Nacional will meet Peruvian club Cesar Vallejo in the last eight, the Trujillo-based club advancing 24 hours earlier after surpassing Brazilian Serie A side Bahia via a penalty shoot-out.
The Colombians reached the quarter-finals in 2013, and will be looking to better that effort and also those of the sides that finished as runners-up in 2002 and made the semi-finals a year later.
River Plate won their first-leg tie away at Libertad 3-1, after two blackouts marred the contest in Paraguay.
The hosts in Asuncion led in the shadows of half-time, as Claudio Vargas netted an injury-time opener.
But Carlos Sanchez equalised - shortly before the second power outage at the Estadio Dr Nicolas Leoz - before Sebastian Driussi and Giovanni Simeone scored more valuable away goals for the Argentine visitors.
The second leg will be held in Buenos Aires on Wednesday.
