The West Brom striker continued on his recent hot streak to become the first Venezuelan to score in three Copa Americas as he rolled home the 36th-minute winner when a long-range shot from Alejandro Guerra was tipped onto the crossbar.
After beating Jamaica 1-0 in their opening match of the tournament, Venezuela have made it through to the quarter-finals with a game to spare.
An impressive feat considering the underdogs currently sit bottom of the South American 2018 World Cup qualifying group with one point from their opening six games.
Uruguay's defeat was their second successive in the group, with Mexico's 2-0 victory over Jamaica confirming their shock exit.
Luis Suarez, who was an unused substitute after injuring his hamstring in Barcelona's Copa del Rey final win over Sevilla, cut a despondent figure throughout the game.
At one point he struck the side of the dugout and allegedly threw one of his boots on to the pitch.
However coach Oscar Tabarez seemed oblivious to Suarez's antics.
"The player is not fit to play," said Tabarez. "I will not select a player who is not 100%. Was he angry? I am not aware. He told me nothing."