Velez Sarsfield hammered compatriots Argentinos Juniors 4-0 in the return match of the second phase - but boss Ricardo Gareca found room for improvement afterwards.
El Fortin were able to build on the goalless draw in the first leg as visitors and never looked back after Guillermo Franco had given them a 23rd-minute lead, heading in following good work from Juan Manuel Martinez.
It was 2-0 in the 55th minute when midfielder Augusto Fernandez stole the ball and advanced into the box before beating Argentinos goalkeeper Luis Ojeda.
Forward Martinez made it 3-0 in the 74th minute with a penalty, before midfielder Hector Canteros rounded off the win with six minutes remaining.
However, boss Gareca said: "We have shown important things on the field, but we have other mistakes to be corrected.
"Argentinos had some opportunities to equalise when we were ahead 1-0. We were in need of a victory like this one."
In Santiago, Chilean giants Universidad Catolica made an important step towards the round-of-16 as they defeated compatriots Iquique 2-1 in the first leg.
Milovan Mirosevic headed in Rodrigo Valenzuela's cross to open the scoring in the 37th minute, with Enzo Endia widening the gap six minutes into the second half.
However, Michael Rios reduced the deficit in the 81st minute - a goal which may prove crucial with the return match scheduled for Wednesday.