After a goalless first half, Luis Bolanos opened the scoring in the 47th minute before Hernan Barcos sealed the points 11 minutes later. Godoy Cruz midfielder Carlos Sanchez was sent off in the 62nd minute for a foul on Ezequiel Gonzalez, leaving the Argentinian side's hopes of claiming the win they needed to advance in tatters.
Barcos told Fox Sports: "I'm very happy to have progressed and to have scored. Godoy Cruz did their job well in the first half and we did not manage to hurt them. The early goal in the second half was very important, it helped us a lot."
Argentinian giants Independiente needed to score eight goals against Penarol in Uruguay and hope Liga and Godoy Cruz drew. The Red Devils fell seven goals short, winning 1-0, and will now have to watch the rest of the competition on the television.
Facundo Parra finished from Roberto Battion's assist in the 33rd minute to help Independiente claim a consolation win at the Estadio Centenario.
With seven minutes remaining, Penarol striker Juan Manuel Olivera headbutted Independiente defender Ivan Velez and was shown the red card. Independiente keeper Fabian Assmann was also dismissed for pushing Olivera, meaning Parra finished the game in goal for Independiente.
"It's a pity that we won in Uruguay but failed to qualify. We're happy we did our job well here, but we should have clinched better results at home," said Parra. Penarol had already qualified.
Tachira went ahead thanks to a fourth-minute goal by Edgar Perez-Greco, but Diego Rubio finished from Jose-Pedro Fuenzalida's pass four minutes later to equalise. In the 23rd minute, Rubio chested the ball down and sent it into the back of the net to give Americo Gallego's side the win.
Colo Colo took the lead in Group 5 on nine points, one more than Paraguay's Cerro Porteno.