Ramon Abila scored the opening goal of the second leg with a powerful finish in the 57th minute.
The hosts sealed their win deep into additional time through Eduardo Salvio as they moved into the last eight, where they will face Ecuadorian outfit LDU Quito.
Gabriel Barbosa, on loan from Inter, struck twice in the opening 19 minutes – including from the penalty spot – to bring the tie level at 2-2 on aggregate.
Diego Alves, who developed a reputation for saving penalties during his time with Valencia, saved from Dixon Arroyo in the shoot-out before Nicolas Queiroz hit the crossbar, sending Flamengo through.
Next up for Flamengo are Internacional, who claimed a 2-0 win at home to Nacional to wrap up a 3-0 aggregate success.
Cerro Porteno set up a quarter-final meeting with defending champions River Plate thanks to a come-from-behind 2-1 win over San Lorenzo in Asuncion, after their first leg finished 0-0.