João Cancelo, Gonçalo Ramos, Vitinha and João Félix were on target for Jorge Jesus’ side, who twice surrendered the lead before finding the goals that secured all three points.
The victory came in Portugal’s first match since Cristiano Ronaldo left the national team camp, placing additional attention on how the side would perform without their captain.
Cancelo and Ramos put Portugal ahead
Portugal made a bright start and took the lead in the 13th minute. Gonçalo Ramos provided the assist for Cancelo, who exchanged passes with the striker before lifting a composed finish over Denmark goalkeeper Mads Hermansen.
Denmark responded in the 23rd minute through Mikkel Damsgaard. The Brentford midfielder finished a swift attacking move with a superb effort into the top corner to make it 1-1.
Portugal restored their advantage just two minutes later. Bruno Fernandes supplied the pass for Ramos, who finished to put the visitors 2-1 ahead.
However, Denmark remained dangerous and found another equaliser early in the second half. Rasmus Højlund struck in the 53rd minute after being set up by Damsgaard, bringing the score to 2-2.
Vitinha and Félix seal the win
Portugal regained the lead in the 67th minute when Vitinha headed home Bruno Fernandes’ delivery, putting the visitors 3-2 ahead.
Denmark continued to search for another response, but Portugal defended their advantage before adding a fourth goal late in the match.
João Félix completed the scoring in the 87th minute, finishing after a pass from substitute Diogo Dalot to seal a 4-2 win for the visitors.
Portugal maintain perfect record
The result gave Portugal a third consecutive victory in Group A4, taking them to nine points from three matches.
Denmark, meanwhile, remained on three points after suffering their second defeat of the campaign.
Portugal will look to extend their winning run when they face Hungary in their next Nations League fixture, while Denmark will aim to respond against Norway.
Full-time result
• Denmark: 2 – Mikkel Damsgaard 23', Rasmus Højlund 53'
• Portugal: 4 – João Cancelo 13', Gonçalo Ramos 25', Vitinha 67', João Félix 87'
Portugal’s attacking quality proved decisive in Copenhagen, as they recovered from two Denmark equalising goals to claim a valuable away victory.