Michael Quinonez and Matias Oyola starred for Barcelona at their home ground with each scoring a goal, while they compiled three assists between them.
Oyola set up Jose Perlaza for Barcelona's first goal of the game after a quarter of an hour before also providing the crucial pass for Quinonez to make it 2-0 in the 32nd minute.
Just before half-time, Oyola also got on the scoresheet, making no mistake from the penalty spot.
In the 52nd minute, Holger Matamoros scored Barcelona's fourth goal and 13 minutes later, Quinonez set up Brayan de la Torre.
A penalty from Cesar Gonzalez gave Deportivo Tachira a consolation goal in the 81st minute.
After a scoreless first leg, Barcelona's four-goal victory on Wednesday handed them a win on aggregate and a spot in the second round.
In Wednesday's other match, Cerro Porteno smashed O'Higgins 4-0 to complete a 7-3 victory on aggregate.
The Paraguayan hosts needed just 15 minutes to take the lead against their Chilean opponents thanks to a goal from midfielder Jonathan Fabbro.
Cerro doubled their lead just a minute later when Fidencio Oviedo hit the back of net to put his side 5-3 up on aggregate.
Santiago Salcado made it 3-0 in the 74th minute before Alejandro Da Silva finished off a poor match for O'Higgins with a goal in the 90th minute.