Universidad de Chile also needed penalties to go through against Paraguay's Libertad following a 1-1 draw in the other tie.
Santos, who won 4-2 on penalties, will face Corinthians in an all-Brazilian semi-final while Boca take on Universidad.
Velez, beaten semi-finalists last season, took a 1-0 first-leg lead to Santos and set out with the clear intention of frustrating the Brazilians with blanket defence.
As in the first leg, the Argentine side managed to keep Santos forward Neymar largely under wraps.
However, Neymar's first real contribution in the 39th minute left Velez with 10 men. The Mohican-haried 20-year-old burst through the Velez midfield and was denied a clear shot at an empty goal when was upended on the edge of the area by goalkeeper Marcelo Barovero, who was sent off.
Elano wasted the resulting free-kick as he sent his effort over the bar.
Santos continued to find it hard going after the break with Alan Kardec bursting through in the 74th minute, only to see his effort blocked by new goalkeeper German Montoya
Santos finally broke through three minutes later, opening up the Velez defence with a quick combination between Paulo Henrique Ganso and Leo, before Kardec fired into the bottom corner.
In Santiago, Universidad de Chile, who managed a 1-1 draw away in the first leg, got off to a flying start when Marcelo Diaz scored with a free-kick which went under the Libertad wall in the 17th minute.
But an own goal by Osvaldo Gonzalez, who inadvertently headed in a Libertad free-kick in the 22nd minute, meant they had to start all over again.
Playing a dynamic passing game inspired by former Chile coach Marcelo Bielsa, the hosts dominated the second half but found Libertad goalkeeper Rodrigo Munoz in outstanding form.
However, Munoz was powerless as the Universidad converted all five of their penalties in the shootout while his opposite number Johnny Herrera was the hero, stopping Victor Ayala's effort as the Chilean champions won 5-3 in the shootout.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.