Forward Juan Manuel Martinez scored a hat-trick, with his second goal quite superb, dribbling two defenders close to the goal line and spooning the ball over the goalkeeper from the tightest of angles.
Uruguayan striker Santiago Silva converted two penalties to lead the championship scorers jointly with team mate Martinez with six goals apiece and substitute Jonatan Cristaldo rounded off the rout.
Velez are five points behind leaders Estudiantes, who beat Olimpo 2-0 on Friday, with nine matches remaining.
Arsenal are equal with Velez on 20 points after a last minute goal by striker Mauro Obolo gave them a 1-0 home win over Banfield.
Independiente's new coach Antonio Mohamed marked his start at the helm of the ailing giants with a much-needed 1-0 win over Racing Club in the Avellaneda derby, the second biggest game in Argentine football after River Plate v Boca Juniors.
"(The players) played like fans which is what we asked them as soon as we committed ourselves to pulling Independiente out of this bad situation in which we found them," said Mohamed, who took charge on Tuesday and found confidence was low in the squad.
Independiente had won only one match in nine. They are now 17th in the standings with nine points. Racing have 13 points.
Paraguayan defender Cristian Baez, in only his third first division match and first for Independiente, scored the only goal against the run of play just before halftime when he headed home midfielder Leandro Gracian's corner from the right.
"I couldn't believe it, I didn't know how to celebrate it (the goal), but I'm happy because it won the 'clasico'," Baez told reporters.
Racing dominated the match but were kept out by their former goalkeeper Hilario Navarro.
"He had the perfect match, he kept out everything we threw at him... Racing proposed and left with their hands empty," Racing coach Miguel Angel Russo said.
