Velez consolidated their Group Four lead after defender Sebastian Dominguez opened the scoring early in the 7th minute.
Lucas Romero doubled the lead after 19 minutes with a shot form distance.
Iquique reduced the deficit through Manuel Villalobos in the 39th minute, but Colombian forward Jonathan Copete made it 3-1 for Velez five minutes after the interval.
Velez keeper Sebastian Sosa also saved a Rodrigo Diaz penalty during the first half.
Romero told Fox Sports it was "a very hard match".
He added: "We knew it was a must-win game for us in order to get the qualification so we are very happy with this result.
"We are relaxed in the Copa Libertadores ahead of the last group game because we are already qualified. Now, it is time to focus on the local league."
Ecuador's Emelec went up to second in the group on nine points, three behind Velez, thanks to a 2-0 home win over Uruguayan giants Penarol, who remain third on six.
With only nine minutes to go, Argentinian defender Cristian Nasuti headed a free-kick into the back of the net, while Fernando Gaibor extended the lead with a goal from a free-kick in injury time.
Emelec need a draw against Velez Sarsfield in their next game to progress.
Penarol, meanwhile, take on already-eliminated Iquique in Montevideo and will keep an eye on Emelec's result as it effects their qualification hopes.
Colombian side Tolima did not feel the effects of altitude as they beat Peruvian team Real Garcilaso 3-0 at 3,300metres above sea level.
Paraguayan forward Rogerio Leichtweis netted a hat-trick, scoring in the 54th, 66th and 84th minutes to put his side second in Group Six.
Only goal average places Tolima above Real Garcilaso, with both sides even on seven points.
Colombian side Santa Fe lead Group Six after beating Paraguayan outfit Cerro Porteno 1-0 in Bogota to reach the eight point mark.
Jefferson Cuero gave Santa Fe the win after 23 minutes as he chested down a Yulian Anchico cross into the back of the net.
With 15 minutes remaining, Santa Fe defender Carlos Valdes and Cerro Porteno midfielder Fidencio Oviedo were both shown a red card.
Following the defeat Cerro Porteno have no chance to make it into the next round.
Brazilian giants Palmeiras saw off Argentina's Tigre 2-0 at home to climb up to second in the Group Two standings.
Caio opened the scoring after 20 minutes, after being set up by Vinicius, and Charles added a second early in the second half.
Palmeiras have collected six points so far, two less than Paraguayan side Libertad and one more than Peru's Sporting Cristal. Tigre lie bottom of the group on three points.