The result means Peru qualify from Group B in second place behind hosts Brazil, along with Colombia and Ecuador. Venezuela were eliminated, finishing bottom after failing to register a win in the group stages.
Ecuador edged above Venezuela in the group by managing to claim a draw in the evening's other game against regional giants Brazil, who failed to win for the first time in 11 games but still qualified top in the group for the quarter-finals.
Peru's André Carrillo gave his team the lead after 48 minutes, firing high into the net from close range after a corner led to a goalmouth scramble at the empty Mane Garrincha stadium in Brasilia.
Venezuela could count themselves a tad unlucky as the ball ricocheted around the penalty area, including off a Venezuelan defender, before being swept into the net by Carrillo, who had also salvaged a draw in the previous game against Ecuador.
The win ended a run of drawn games between the two South American countries going back to another 1-0 Peru victory at the Copa America in 2015.