Guerrero treble seals third place for Peru
William Chiroque put Peru ahead from Guerrero's pass three minutes before half-time and the striker nicknamed "Predator" rammed home the second in the 64th and two more in added-time.
"Third place is very good, I'm very proud of this team," Guerrero told a TV reporter before the medals ceremony.
"I'm a forward and I have to score goals, I work for the team. For me it's more important that the team wins," Guerrero said after becoming top scorer at the tournament with five goals.
Peru, who began the tournament as outsiders but improved with each match while favourites Argentina, Brazil and Chile fell by the wayside, contributed to one of the best matches.
"Peru played a much better match than us. Peru were a great team that knew how to take advantage of our mistakes," said Venezuela's coach Cesar Farias.
Venezuela, who had midfielder Tomas Rincon sent off on the hour for a dangerous tackle on Carlos Lobaton, pulled a goal back when midfielder Juan Arango poked home in the 79th minute at the end of a counter-attack.
Four minutes later Venezuela, also outsiders at the start of the tournament, could have equalised when Peru goalkeeper Raul Fernandez was unable to hold Arango's fierce free-kick but left-back Gabriel Cichero put the rebound just outside the post.
With Venezuela committed to trying to equalise, Guerrero hit them with two more goals in late breakaways, showing great control and exquisite finishing in both to cement his place as one of the best strikers of the competition.
Nippy forward Chiroque could have scored in the 27th minute but goalkeeper Renny Vega blocked his shot from a tight angle when a pass to the unmarked Paulo Cruzado would have been the better option.
However, Guerrero helped break the deadlock before the interval when he exchanged passes with midfielder Cruzado before crossing from the right to the far post where Chiroque steered the ball home past the committed Vega.
Peru's second and Guerrero's first goal came soon after Venezuela were left with 10 men when he took Chiroque's pass and calmly measured his shot into the roof of the net.