Jose Ortigoza, Victor Mareco and Daniel Guiza were on target as Porteno scored three unanswered goals to triumph 3-1 on aggregate in Paraguay on Tuesday.
Porteno will face defending champions Lanus of Argentina in the round of 16.
Returning home from Ecuador trailing 1-0, Porteno set out to erase the deficit and they did so before half-time after Independiente striker Daniel Angulo was sent off in the 20th minute at the Estadio Defensores del Chaco.
Ortigoza levelled proceedings on aggregate, breaking the deadlock in the 34th minute after placing the ball beyond Independiente goalkeeper Librado Azcona with the outside of his foot.
The home side - fourth in Paraguay's Division Profesional - doubled their lead 11 minutes into the second half, an unmarked Mareco allowed enough time to control the ball and fire into the back of the net.
Former Spain international Guiza sealed the victory 10 minutes later, played in by Oscar Romero before coolly converting underneath Azcona.
Peruvian side Cesar Vallejo were also 3-0 winners, accounting for Club Universitario at the Estadio Mansiche.
Second-half goals from Donald Millan, Andy Pando and Daniel Chavez saw Vallejo win 5-2 on aggregate against their Bolivian opponents.
Brazilian outfit Bahia await Vallejo in the next round.
After a goalless opening half, Millan made the breakthrough in the 56th minute with a free-kick.
It got better for the hosts six minutes later, when Pando won the ball inside the penalty area and cheekily back-heeled past Universitario goalkeeper Juan Robledo.
Chavez put the icing on the cake with eight minutes remaining, lobbing the ball over the onrushing Robledo from the edge of the box.