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Jose Pekerman's men had a great chance to take the lead in the opening stages of the match when Radamel Falcao turned his man and drilled a low effort towards the bottom corner, but Pedro Gallese was there to make a fine save.
Colombia threatened again minutes later when Falcao threaded a through-ball into the path of Santiago Arias, who burst into the box down the left inside channel, but his strike went into the side-netting.
Sanchez had another opportunity moments later as Colombia were guilty of giving the ball away once more, but David Ospina bailed his teammates out with a fine diving stop.
Pekerman's side responded to the threat when James Rodriguez and Teofilo Gutierrez combined to create an opening for the Real Madrid man. Rodriguez's shot was well saved by Gallese, but the loose ball fell to Jackson Martinez, although he blasted the ball wide.
Both sides pushed in the dying minutes, but neither could break the deadlock, which was enough to see Peru reach the quarter-finals of the competition, while Colombia need either Brazil or Venezuela to record a victory in their match later today in order to advance.