Miguel Villalta opened the scoring after 27 minutes, Carlos Marino added the second in the 70th minute, and Hamburg's Paolo Guerrero completed the rout one minute from time.
Peru's win gave them the summit of Group A with 3 points, while Uruguay are dumped to bottom with no points.
In the competition's opening game, Bolivia registered a 2-2 draw with hosts Venezuela, with the presence of the latter's president Hugo Chavez and Argentine legend Diego Maradona in San Cristobal.
The home fans went mad when Giancarlo Maldonado gave Venezuela a 21st minute lead, but the goal was cancelled out with a 39th minute strike from Bolivia's Jaime Moreno.
The hosts went in front for the second time through Ricardo Paez, the son of Venezuela coach Richard Paez, nine minutes after the break.
However, Juan Carlos Arce equalized seven minutes from time to deny Venezuela their second ever win in the competition's history.
Bolivia and Venezuela share second place on one point, two adrift of group leaders Peru.