The result at the Estadio General Pablo Rojas in Asuncion was enough for Daniel Farias' men to edge through 4-3 on aggregate.
Deportivo Tachira take their place in Group Eight, which also consists of Sporting Cristal, Racing and Guarani.
Cerro Porteno, who suffered a 2-1 first leg loss, took the lead on Wednesday thanks to Jonathan Fabbro's well-placed 40th-minute penalty.
But Rivas struck 10 minutes into the second half, placing in from close range after Pablo Olivera played him in.
The hosts regained the lead and levelled the tie just after the hour-mark.
Cecilio Dominguez brought down a Fabbro cross with his chest before firing in from the middle of the penalty area.
Just a minute later and Rivas scored again, firing a 25-yard effort into the bottom corner for what proved to be a key goal.
Corinthians eased into the group stages, completing a 5-1 aggregate win over Once Caldas with a 1-1 draw in Colombia.
Elias put the Brazilians even further ahead in the tie and Johan Arango's second-half goal meant little.
Corinthians take on fellow Brazilians Sao Paulo, San Lorenzo and Danubio in Group Two.
