Rasmus Hojlund earned Denmark a deserved 1-0 lead over Portugal in their Nations League quarter-final first leg clash on Thursday.
The Manchester United forward delivered from the bench to split the teams in Copenhagen, providing the finishing touch Denmark previously lacked on a night where they dominated Roberto Martinez's side.
The Spanish coach selected veteran Cristiano Ronaldo, 40, up front but the Al-Nassr striker was mostly frozen out of the game.
Winners of the inaugural tournament in 2019, Portugal are aiming to become the first team to lift the Nations League trophy for a second time.
However they will need to improve swiftly to reach the semi-finals as Denmark outclassed them and could have scored more on the night.
Looking for their first win under coach Brian Riemer, who was appointed in October, the Danes were without injured captain Pierre-Emile Hojbjerg.
Denmark piled on the pressure from the start, with debutant Mika Biereth charging down Diogo Costa's clearance, but the goalkeeper managed to escape with conceding only a corner.
Jesper Lindstrom forced Costa into action again with an effort from distance, while Pedro Neto tested Kasper Schmeichel at the other end.
The hosts won a penalty when Portugal defender Renato Veiga handled the ball but Costa produced a superb save to deny Christian Eriksen.
The Porto goalkeeper, an expert in saving spot kicks, dived low to his right to thwart the Manchester United midfielder.
Costa made another stunning save from Biereth to keep his team level, as Denmark turned the screw.
When the hosts finally beat Costa, Diogo Dalot was in the right place at the right time to clear Eriksen's effort off the line just before the break, after good work by Gustav Isaksen.
Riemer's side stayed on top in the second half, with Costa saving an Eriksen free-kick, although Vitinha came close for Portugal, who showed occasional flashes of their quality on an otherwise lethargic display.
Isaksen, a constant menace for Denmark, had a shot deflected behind as Denmark started to fear their dominance would not translate into a lead. However Hojlund, on as a substitute, had other ideas.
The striker, who ended a long Manchester United drought last weekend by scoring in his team's win at Leicester City, broke the deadlock by slotting home to cap a fine move.
Eriksen spread the ball to another substitute, Andreas Skov Olsen, who picked out Hojlund with a low ball to finish coolly in the 78th minute.
Portugal's Bernardo Silva, making his 99th appearance for his country, had a penalty appeal late on waved away after falling under pressure from Patrick Dorgu in the box, and Schmeichel saved from Neto in the final stages.
Portugal host Denmark in the second leg in Lisbon on Sunday.
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