The Ecuadorian outfit travelled to Guarani with a 1-0 lead from last week's first leg and were on track to progress with Thursday's contest scoreless at half-time.
A 62nd-minute effort from Guarani's Marcelo Palau levelled the tie on aggregate, leaving Independiente's progression in doubt, but Jose Angulo scored the all-important equaliser 14 minutes from time to put Independiente 2-1 up on aggregate.
Rodrigo Lopez netted five minutes later for Guarani, who moved 2-1 ahead on the night, but Angulo's goal proved the difference with the scores locked at 2-2.
Independiente now join Group 5 alongside Atletico Mineiro, Colo Colo and Melgar.
Elsewhere, Santa Fe eased past Oriente Petrolero 3-0.
The Bolivian side had it all to do when they made the trip to Bogota having lost 3-1 at home and it only took 39 minutes for Santa Fe to seal the win.
Two goals from Yerry Mina in six minutes before the break put the home side in control.
And Anthony Otero capped the result and a 6-1 victory on aggregate with his 74th-minute strike.
Sante Fe enter Group 8 with Cerro Porteno, Cobresal and Corinthians.