The Hamburg player netted the crucial second strike midway through the second-half, which came six minutes after Venezuela had been reduced to 10 men following club colleague Tomas Rincon's red card. Guerrero then added a further two goals to put the icing on the cake.
"We fought and we were strong when it mattered," he told ESPN after the game. "I am proud to be Peruvian. We enjoyed the tournament although we could have got a little more out of it.
"Third place is fine. I am very proud of this team. I work for the group and the important thing is the team. I scored three goals and I'm very happy."
Formerly with Bayern Munich, Guerrero is the tournament's leading goalscorer to date with five strikes to his name and was also named the man of the match in the group game against Uruguay.
"Third place is a good achievement. As for being the top scorer, I am the main striker and I can say that scoring goals is my job. Most of all, I am glad to have made a contribution to this side."
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