Trailing 2-0 heading into the return leg in Paraguay, Nacional left it late as they beat General Diaz 3-1 at the Estadio Feliciano Caceres.
Santiago Trellez was the hero for Nacional, scoring two minutes from time as the Colombian giants prevailed 3-3 on away goals, setting up a last-16 showdown with Brazilian side Vitoria.
Nacional - unbeaten in 11 games on the road in all competitions prior to kick-off - quickly reduced the deficit after Edwin Cardona opened the scoring from long range in the 13th minute.
Cardona, however, went from hero to villain in the space of 15 minutes, sent off for a second bookable offence.
General Diaz restored their two-goal advantage thanks to Roberto Gamarra on the hour-mark.
That is as good as it got for the hosts as Nacional scored two unanswered goals.
Wilder Guisao put Nacional ahead on the night three minutes later, firing the ball beyond Bernardo Medina, before Trellez netted the tie-winning goal in the 88th minute.
Meanwhile, Ecuadorian outfit Emelec joined Nacional in the round of 16.
Emelec and River Plate exchanged first-half goals in Uruguay, with Angel Mena and Leandro Rodriguez on target in the 1-1 draw at the Estadio Luis Franzini.
The draw was enough for Emelec, who progressed 3-2 on aggregate.
Emelec will go head-to-head against Goias of Brazil for a spot in the quarter-finals.
