Wilfredo Olivera saw red for the host on the stroke of half-time, and Velez took advantage with Facundo Ferreyra netting the only goal in the 57th minute.
Velez is now four points clear of Newell's Old Boys, having played a game more.
Substitute Leonel Nunez scored a last-gasp winner as Argentinos Juniors beat Estudiantes 2-1.
Pablo Barzola had given Juniors an 18th minute lead but that was cancelled out by Duvan Zapata just before the hour mark.
Struggling Union Santa Fe picked up only its fifth point of the season as it drew 2-2 at home with San Lorenzo, despite the late dismissal of Maura Angel Maidana.
It fell behind to a Denis Stracqualursi penalty after 10 minutes but was quickly level through Andres Franzoia before snatching a lead on the stroke of half-time when Bruno Bianchi found the net.
Fabian Bordagaray levelled four minutes into the second half, but Union hung on for a rare point, despite being reduced to 10 men in the final minute.