The tie ended 1-1 on aggregate but Santos triumphed 4-2 on penalties to set up a meeting with fellow Brazilian side Corinthians in the semi-finals.
Trailing 1-0 from the away leg it was down to Santos to take the initiative but Muricy Ramalho's side struggled.
In the 39th minute Brazilian star Neymar controlled a long ball and was fouled just outside the area by Argentinian keeper Marcelo Barovero who was sent off.
Santos tried to press home their numerical advantage after the break but substitute goalkeeper German Montoya denied Adriano and Ganso.
Velez went close but Augusto Fernandez's long-range shot and a close effort by Juan Manuel Martinez were well saved by Rafael.
But the home side levelled up the tie on aggregate through Alan Kardec after good work by Ganso and Elano.
In the penalty shootout keeper Rafael kept out Emiliano Papa's effort.
"Velez were very difficult rivals, but I think we deserve the qualification. Now we have to work harder because Corinthians will be a harder challenge," said Rafael.
"I know that some people want us to play in a bigger stadium but we must be hosts here in Vilha Belmiro. Here the pressure for the visitors is huge."
With the clash between Corinthians and Santos, Brazil is guaranteed to have a team in the final for the eighth consecutive year.
The other team to clinch their semi-final spot was Universidad de Chile who defeated Paraguayans Libertad 5-3 on penalties after the tie ended 1-1.
Marrcelo Diaz put the hosts ahead with a precise free-kick after 18 minutes but four minutes later the sides were level due to an Osvaldo Gonzalez own goal.
Chilean keeper Johnny Herrera made several important saves, including from the last move in normal time when he stopped a powerful shot by Rodolfo Gamarra.
In the shootout Herrera saved from Victor Hugo Ayala.
The reward for Jorge Sampaoli's side is a tough semi-final against Argentinian side Boca Juniors.