Maxi Moralez put Velez ahead in the first half and Juan Manuel Martinez scored twice in the last 15 minutes.
"It's a pleasure playing with these team-mates," Martinez said. "We're making a big effort and luckily we see that in the results.
"We won't be relaxed (in the second leg). They're a great team and, just as we scored three tonight, they can do it at their home. It will be very tough."
Cerro Porteno, the other Paraguayan team in the competition, fared better with a 1-1 draw away to Mexico's Jaguares. And it took a last-minute equaliser from Antonio Pedroza to deny the visitors the win after Jonathan Fabbro had opened the scoring in the 72nd minute.