And despite Peru's impressive attacking play, they could not break down the Danish defence, leaving themselves with a big task ahead of their second Group C game against France on June 21.
Peru began the fixture at a fast pace and they got their first shot on target as early as the eighth minute through Yoshimar Yotun, whose 25-yard strike went straight into the hands of Kasper Schmeichel.
The Leicester City man repelled everything thrown at him, and he had plenty to do.
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The win gives Denmark a good chance of qualifying for the knockout stages, and in Schmeichel they have a solid foundation on which they can build their hopes of going deep into the tournament.
The teams were level after an interesting first half in which Peru missed a penalty.
Ricardo Gareca's pacy side took the game to Denmark and were certainly not afraid to shoot on sight.
Cueva had the best chance to open the scoring just before half-time when Peru were awarded a penalty.
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He proved integral again, setting up Poulsen for the opening goal with a superb pass that left the striker with only the goalkeeper to beat.
Denmark made them pay two minutes later on the counter-attack as Christian Eriksen laid the ball of for Poulsen to finish inside the near post.
Within the opening minutes of the match, Peru was pushing forward and almost drew a penalty when Flores and Poulsen collided on the left side of the area, but Gassama waved play on.
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The ship was eventually rerouted to Spain, after Spanish authorities said it would be allowed to dock in Valencia. Conte said he and Macron "agreed on the need to cooperate closely" on migration issues.
Neither team created any clear-cut chances until the last couple of minutes of the half, where a penalty was given after a VAR review.