La Plata opened the scoring midway through the first half through Rodrigo Contreras, but Lucas Pratto levelled matters five minutes after half-time before Hector Canteros gave Velez the lead in the 68th minute.
The visitor was dealt a blow by Ricardo Diaz's red card shortly afterwards and Velez capitalised with ruthless efficiency with three goals in the last 15 minutes.
Mauro Zarate netted from the spot to double the home side's lead and added his second in the final minute shortly after Agustin Allione had put the result beyond doubt.
Substitute Gonzalo Rios scored late on to grab a 1-1 draw for Quilmes at Newell's Old Boys, which had opened the scoring through David Trezeguet.
The former France international, who bagged a brace in the Copa Libertadores victory over Nacional earlier this week, netted in the 78th minute - 10 minutes after coming off the bench - but Rios ensured second-bottom Quilmes earned a share of the spoils after scoring in the 89th minute.
Luciano Vietto struck seven minutes from time to rescue a 2-2 draw for Racing Club at Atletico Rafaela.
The visitor had taken a 51st-minute lead through Rodrigo De Paul and although quickfire goals before the hour mark from Lucas Albertengo and Adrian Bastia had put Rafaela in control, until Vietto grabbed a point for Racing Club.