Silvio Torales' 84th-minute goal lifted Asuncion to a 3-2 victory at the Estadio Defensores del Chaco.
The result was enough for Asuncion (eight points) to claim second spot after Venezuela's Zamora (seven) lost 1-0 at group leaders and Brazilian giants Atletico Mineiro (12) on the final matchday of the second round.
Santa Fe of Colombia started the day level on five points alongside Asuncion but they moved towards the next round courtesy of Wilder Medina's 31st-minute opener.
Their joy was short-lived, however, as the Paraguayans hit the front thanks to Julian Benitez and Fredy Bareiro, who found the back of the net within 10 minutes of each other.
Medina threw a spanner into the works, converting a penalty eight minutes from time.
But Torales secured Asuncion's passage into the final stages of South America's continental competition with the match-winner two minutes later.
At the Estadio Governador Magalhaes Pinto, a 10th-minute strike from Brazil international Jo was enough as Mineiro downed 10-man Zamora 1-0.
In other results on Thursday, Newell's Old Boys crashed out of the competition following their 3-1 defeat at the hands of Atletico Nacional.
Newell's were in the box seat to progress from Group Six, with the Argentinean outfit one point ahead of Atletico Nacional in second spot heading into their do-or-die clash.
But Atletico Nacional leapfrogged their opponents thanks to goals from Santiago Trellez, Sherman Cardenas and Orlando Berrio.
The Colombians finished on 10 points, two ahead of Newell's (eight).
Brazilian team Gremio topped the group on 14 points following their narrow 1-0 win at home to winless Nacional (one) of Uruguay.
In Group Eight, Arsenal routed Santos Laguna 3-0 in their final group fixture.
Both teams had already qualified from the group but Arsenal claimed a convincing win over the group leaders courtesy of strikes Emilio Zelaya, Mariano Echeverria and a Marc Crosas own goal.
Mexico's Laguna (13) and Arsenal (12) of Argentina finished well ahead of Penarol and Deportivo Anzoategui (both on five points), who played out a 1-1 draw.
