The change helped Eriksen find more space as the Danes started playing more passes and he showed what he is capable of during a fast counter-attack when he threaded a ideal pass to Yussuf Poulsen, who beat Peru goalkeeper Pedro Gallese to score.
"He is fast on his feet and his goal line play is probably the best in the world when he is in form".
VAR then intervened, and referee Bakary Gassama awarded the spot-kick.
"After the penalty he was asking for the ball, participating in play - that's the only way".
Saturday's match is important for both sides as they are fighting for the second spot for qualifying for the Round of 16, while France, also in Group C, are tipped as the most hopeful for the top spot.
The 64-year-old, who fears midfielder William Kvist could be ruled out for the rest of the World Cup having come off in the first half with a suspected fractured rib, said: "I think Peru is an outstanding team.
This team has been playing together well (without him)", he said.
The joy at the final whistle for Denmark was contrasted with the agony for Peru and especially Cueva, who was consoled by team-mates on the pitch both at half-time and at the end of the game.
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Mickelson played the third round with England's Andrew "Beef" Johnston, who had a hard time believing what he was seeing. Shinnecock Hills has been ripping apart the world's best players all week and it all must have just gotten to Mickelson.
Eriksen is clearly the key to Denmark's hopes, but they will need more from their other attacking players to make a real impact on the tournament.
Within his first two minutes on the field, his point-blank header was saved by Schmeichel.
That aggressive play led to Peru winning a penalty late in the first half on an attempted tackle by Yussuf Poulsen on Edison Flores.
Peru finished with 17 attempts to Denmark's 10, and numerous Incas' shots were of the point-blank variety.
The Danish side that ended the Republic of Ireland's hopes of qualifying for the World Cup with a play-off victory last November needed some smart saves from keeper Kasper Schmeichel and desperate defending at times, but they navigated a route to victory with a 59th minute victor.
Peru had by no means lost hope, he added, ahead of facing France on June 21 and Australia five days later. "I don't think Peru deserved to lose but we can't cry over spilt milk".
However, the indomitable Peruvian spirit is unlikely to be dampened, and they will take the party to Ekaterinburg where they face France on Thursday. Schmeichel dove to his right to bat the ball away.
After failing to qualify for the World Cup in 2014 and Euro 2016, there is a strong belief in the Danish camp that they can pull off an upset this summer, and Fabregas believes any success will be down to Eriksen.