Both sides struggled to create clear opportunities in a game bereft of quality, but the result was enough for Ricardo Gareca's side to advance to the last eight
Peru are through to the quarter-finals of the Copa America after drawing 0-0 with Colombia on Sunday night.
Both sides came into Sunday's clash in Temuco hoping to guarantee their spot in the knockout phase, though Colombia needed a win to do so.
Neither side could find the breakthrough in an even encounter, despite Colombia's wealth of attacking talent creating the better chances to break the deadlock.
Radamel Falcao, James Rodriguez and Jackson Martinez all wasted opportunities to be the match-winner for the 2014 World Cup quarter-finalists.
Jose Pekerman's men - who suffered a shock defeat to Venezuela in their tournament opener – were put under pressure at the back by a Peru side that has performed above expectations and will finish at least third in the pool, with a record good enough to advance even if they are nudged out of the top two places.
Colombia, though, will watch on anxiously as Brazil and Venezuela face off in Santiago – a draw in that game will see them eliminated at the first hurdle.
Knowing they needed to force the issue, Colombia were fast out of the blocks and Falcao went close to opening the scoring in the fourth minute as his low shot was tipped round the post by goalkeeper Pedro Gallese after Peru had failed to clear their lines from a corner.
Pablo Armero then lashed into the side-netting before Colombia suffered a blow when Edwin Valencia landed awkwardly when chasing the ball, leading him to being taken off on a stretcher and replaced by Alexander Mejia.
Peru were rarely threatened for the remainder of the half after weathering the early storm and could have taken the lead themselves in the 43rd minute had Paolo Guerrero not skewed wide from Claudio Pizarro's clever pass.
Joel Sanchez saw two good chances to give Peru the lead go begging after the restart as the midfielder fired wide of the near post and was then denied by Colombia goalkeeper David Ospina.
Ospina got down low to his left to keep out Sanchez's first-time effort following great work from Christian Cueva.
The best chance of the second half fell to Martinez, who was thwarted on the rebound by Gallese in the 69th minute after the shot-stopper had prevented Rodriguez from giving Colombia the lead at the end of a quick counter-attack.
And Colombia may be left to rue missing what was their last real opportunity to take all three points, leaving one of the tournament favourites facing a nervous wait to learn whether they will re