Flamengo forward Guerrero, who has spent the past three years in Brazil after spells in Germany with Bayern Munich and Hamburg, pounced in the 20th and 23rd minutes to snuff out Bolivia's campaign.
The 31-year-old completed his hat trick in the 74th minute, strolling clear of the Bolivian defense to finish nonchalantly. Marcelo Martins scored a late consolation from the penalty spot for Bolivia.
The result sets up the mouthwatering prospect of a semi-final next Monday between tournament hosts Chile and Peru, the latest installment of a ferocious footballing rivalry which began in 1935.
Chile and Peru also fought a long-running legal battle over the two nations' disputed maritime border.
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Peru will head into Monday's showdown brimming with confidence after easing past Bolivia.
The match was effectively settled during a devastating three-minute spell midway through the first half when Peru's superb counter-attacking unstitched the Bolivian defense.
Guerrero grabbed his first of the night in the 20th minute, timing his jump to head home past Bolivia goalkeeper Romel Quinonez after an exquisite cross from the left by Fiorentina midfielder Juan Manuel Vargas.
Midfielder Christian Cueva was the architect, kicking a ball over the top of the Bolivian defense to send Guerrero bearing down on goal.