The Copa was promised a rank outsider in the semi-finals after both of these teams defied the odds to escape their respective groups and advance into the quarters.
Bolivia, who only had one warm-up clash prior to the contest - a 5-0 drubbing by Argentina - finished second behind host nation Chile, while unfancied Peru eked their way into the knockouts in a group comprising Brazil, Colombia and Venezuela.
Both sides went into the contest knowing that an unenviable clash with Chile awaited in the next round, and it was the Peruvians who looked game for a crack at the favourites by dominating the opening stages and netting twice inside 23 minutes.
With five goals, Peru hitman Guerrero topped the goalscoring charts at the last Copa but this edition of the tournament had proven more laborious for him, having gone into this morning's encounter without finding the net in their first three games.
Guerrero, whose barren spell at international level stretched back since November, opened his account for the competition by powering a header past Romel Quinonez from Juan Vargas's cross, before slotting home a second minutes later.
Moments later, it was almost three for the ex-Bayern Munich forward, but Quinonez was on hand this time to keep him out and preserve the two-goal deficit for Bolivia.
The Bolivians were demolished 5-0 by Chile in the final Group A outing - a game that saw their defensive deficiencies ruthlessly exposed, but Mauricio Soria's men responded well to the threat of a second successive rout and finally grew into this clash.
Attack had to be the best form of defence for Bolivia, with the same frailties against Jorge Sampaoli's men surfacing at the other end as Miguel Hurtado almost gifted Peru a third, but Jefferson Farfan's effort cannoned off the outside of the post.
Before the break, Farfan was denied by the woodwork once more after his effort came back off the crossbar as La Verde reached the interval with something to salvage in the second half.
Alcides Pena could have reduced the arrears on the hour mark but, after reaching Martin Smedberg-Dalence's ball, he failed to keep his header below the crossbar as the chance went begging.
Any hopes of an unlikely comeback from Bolivia were ended when Guerrero completed his hat-trick 15 minutes from time by capitalising on some hesitant defending to sprint clear and pick out the bottom corner.
Bolivia reduced the deficit when Marcelo Moreno fired home a penalty after Luis Advincula had brought down Ricardo Pedriel, but it was a comfortable finish to the evening for Peru, who will meet hosts Chile in the last four.