Boca Juniors also won 1-0 at home to Fluminense, who played for nearly an hour with 10 men, to leave the two Argentina-Brazil ties on a knife edge for next week's return matches.
Brazilian sides have dominated this year's Libertadores but their four surviving representatives failed to win a match or score a goal between them this week after Vasco da Gama and Corinthians shared a 0-0 draw in Rio de Janeiro on Wednesday.
Neymar, by far the most exciting of the current crop of Brazilian players, led Santos to an 8-0 drubbing of modest Bolivar last week but found the task of facing Velez in their own stadium a different proposition.
He was not helped by the tactics of his coach Muricy Ramalho, who opted for a safety first approach which left his top player isolated against the solid home defence.
Santos barely got into the first half and Velez scored the only goal by Mauro Obolo headed in Emiliano Papa's in the 35th minute.
The second half was little better for Pele's former club.
Six-times winners Boca dominated their match against the 2008 runners-up Fluminense but had to be content with a single-goal win.
Fluminense had midfielder Carlinhos sent off after only 33 minutes when he was given a second yellow card for handball.
The hosts made the breakthrough six minutes after half-time when Dario Cvitanich founded Pablo Mouche and he scored with an angled left-foot shot.
I think that over the course of the 90 minutes, we could have opened up a bigger difference, we had enough chances to do it," said Boca coach Julio Falcioni.
