An own goal by Velez defender Juan Sabia gave Ricardo Zielinski's side a deserved victory in an impressive display at the Estadio Gigante de Alberdi in the province of Cordoba.
In the 16th minute, Cesar Pereyra crossed the ball from the right, Jorge Velazquez shot and the ball was deflected by Sabia into the back of his own net.
Belgrano went for a second goal to extend their lead in the tie but they could not beat Velez's Uruguayan keeper Sebastian Sosa again.
With 13 minutes remaining, Velez defender Sebastian Dominguez was shown the red card for hitting Carlos Bueno and coach Ricardo Gareca was happy to shut up shop thereafter.
"We proved we wanted to win from the kick-off. With this mentality, we can play a good game in Buenos Aires too. It was a great match by us," Belgrano midfielder Guillermo Farre told Fox Sports.
"In this Belgrano team, there are no individuals. The team as a whole is the talent. We would have preferred winning by a wider margin, but we are happy with the 1-0 score and the way we played tonight [Tuesday]."
The second leg will be played on August 29 in Buenos Aires with the winners facing Chilean side Cobreloa or Colombia's La Equidad in the next round.