Defending champions River needed penalties to overcome Cruzeiro after their round-of-16 tie finished locked at 0-0.
Franco Armani was the hero for River, saving penalties from Henrique and David in the shoot-out in Belo Horizonte.
The goalkeeper stepped up as the Argentine giants claimed a 4-2 shoot-out victory, moving into a last-eight tie against either San Lorenzo or Cerro Porteno.
The Brazilians needed a Raphael Veiga penalty to break the deadlock before further goals from Miguel Borja, Gustavo Scarpa and Dudu.
Godoy Cruz were reduced to 10 men when 18-year-old midfielder Agustin Manzur was sent off for a dreadful challenge in the 88th minute.
In Paraguay, Olimpia could only play out a 1-1 draw with LDU Quito, the result enough for the Ecuadorians to advance 4-2 on aggregate.
LDU Quito received two red cards, with goalscorer Jhojan Julio and unused substitute Edison Realpe sent off.