The referee pointed to the spot upon reviewing video footage and Cueva blazed over, much to the dismay of Peru's sizable travelling support.
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. Yet Cueva struck an bad penalty, leaving the red-and-white clad Peru fans distraught.
And it looked as though the winger turned this fortune in his favour, opening the scoring after 59 minutes, largely against the run of play.
Another chance was squandered soon afterwards when Farfan was teed up on the penalty spot but despite making a clean connection with his shot, Schmeichel managed to stick out a leg to keep the ball out.
"Of course it was an emotional game", Poulsen told reporters.
With 11 minutes left, Guerrero almost scored one of the goals of the early stages of this tournament with the Flamengo forward sending a back-heel towards the far bottom corner from 10 yards, only to watch on as the ball went agonisingly wide with Schmeichel beaten.
But Kvist's game lasted just 32 minutes as he had to come off following an collision with Jefferson Farfan which saw the Peruvian's knee bash into his ribs, forcing him to eventually be taken off on a stretcher.
There are no easy games in South American World Cup qualification, and Los Incas outscored the likes of Argentina, Colombia and Chile to get here. "People make mistakes and we have to try and turn things around".
Though Cueva missed the resulting penalty, VAR ensured one was given in the first place, another point in favour of the system.
The Argentine coach backed Cueva to bounce back from his disappointing evening and said he was impressed by the way the Sao Paulo midfielder performed in the second half.
The Danish have been World Cup regulars since 1986 and have players like Kasper Schmeichel, Christian Eriksen and Andreas Bjelland to boast of. Midfielder Christian Eriksen is expected to lead the Danes after scoring 11 goals in World Cup qualifying match and a hat trick in the decisive playoff that clinched Denmark's place in Russian Federation.
What an journey Peru fans have been on to see their country at the World Cup, after a 36-year absence.
It was a sublime save that secured all three points for Denmark from a game many observers feel they probably deserved to lose.