Guerrero scored twice in three minutes midway through the first half to put the Peruvians in the driving seat in their quarter-final clash in the southern Chilean city of Temuco.
His first was a header from a Juan Vargas cross, his second came on the counter-attack after a corner, and his third arrived in the 74th minute when Bolivian midfielder Danny Bejarano gifted him the ball with a misplaced pass and left him one-on-one with the goalkeeper.
Marcelo Moreno scored a late consolation from the penalty spot after Damian Lizio had been tripped in the box but Peru were never in danger of losing and will face Chile in Santiago on Monday in the first of the Copa semi-finals.
"We’re getting better and better,” said Guerrero, who is closing in on Teofilo Cubillas’ all-time scoring record for Peru.
“Not many people had much confidence in us before this tournament but once again we’re showing that we’re a good side.”
Peru, who also reached the semi-finals of the 2011 Copa America, dominated from the outset and could have been out of sight by the break.
After Guerrero’s early double, his striking partner Jefferson Farfan grazed a post with a low shot and then rattled the crossbar with a curling free kick.
Bolivia’s best chance came from a Moreno header which Peru goalkeeper Pedro Gallese did well to parry.
The Bolivians rallied slightly in the second half and had a good appeal for a penalty turned down after Gallese appeared to bring down midfielder Pablo Escobar as he headed goalwards.
There was no way back for Bolivia after Guerrero completed his treble, however.
(Writing by Gideon Long; Editing by Peter Rutherford)
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