Guerrero scored twice in the first half and once the second as Peru cruised to victory in their quarter-final clash.
Bolivia's lone goal of the match was supplied by forward Marcelo Moreno, who converted a penalty in the 84th minute.
Guerrero put Peru 1-0 up in the 21st minute when he climbed higher than Bolivia defender Cristhian Coimbra to head the ball into the net from Juan Vargas' accurate curling cross.
The Flamengo striker only had to wait two more minutes to score his second goal as Christian Cueva's lob from the halfway line set him up perfectly to slot the ball past goalkeeper Romel Quinonez.
The 31-year-old almost completed his hat-trick in the 26th minute, but his header was brilliantly stopped by Quinonez.
Facing the threat of going 3-0 down looming every time Peru had possession, Bolivia began to fight back and launch own counter-attacks as they looked to get back into the game.
They almost succeeded in cutting Peru's advantage in the 27th minute, but defender Alejandro Morales' scorching shot went a few agonising millimetres over the crossbar.
Morales came close to scoring once again just three minutes later when he headed a free-kick towards the goal. But, he was denied by Peru goalkeeper Pedro Gallese, who pulled off a top class stop on the line to ensure his side maintained their 2-0 advantage.
The two teams continued to create chances as the half progressed, but neither was able to find the back of the net and Peru went into the half-time break with a 2-0 lead.
Nineteen minutes into the second half, Bolivia were livid not to be awarded a penalty when striker Ricaro Pedriel was brought down by a challenge from Gallese.
To add insult to injury, Guerrero increased Peru's lead to 3-0 in the 75th minute when he intercepted a poor pass from Marvin Bejarano's and slipped the ball past Quinonez into the bottom corner.
Moreno gave Bolivia a consolation goal with just six minutes to go as he blasted his penalty shot straight down the middle after Damian Lizio was brought down by Luis Advincula.
Peru have now reached the semi-finals for the second consecutive time and will face hosts Chile in Santiago on Monday.