Portugal's first decent effort on target came in the eighth minute when Pedro Neto let fly with a shot from distance but Kasper Schmeichel got a strong hand to it and conceded a corner as both sides sought to attack at every opportunity.

Playmaker Eriksen was in the thick of the action throughout, and Denmark got a penalty in the 23rd when his left-foot shot was handled by Renato Veiga, but the 33-year-old's spot kick was saved by Costa, who dived to his right to parry the ball away.

Costa again denied Biereth a debut goal in the 36th minute with another fine save and Diogo Dalot came to his keeper's rescue just before the break, clearing an Eriksen effort before it crossed the line.

Despite Costa's fine performance, there was little he could do about Denmark's goal as Eriksen picked out Andreas Skov Olsen on the right of the penalty box and he squared the ball for Højlund to steer it home with his right foot.

Denmark backed off after the goal and invited Portugal to attack but the home side managed to keep Ronaldo's team quiet and take a lead into Sunday's second leg in Lisbon. The winners will meet either Italy or Germany in the semifinals.

"We weren't surprised, we knew they were aggressive and that they would come out strong," said Portugal midfielder Bruno Fernandes. "We lacked aggression and we needed to be stronger in the duels, more intelligent in taking advantage of the depth.

"We have a difficult game ahead of us but we really want to win, and at home with our fans we are sure that we'll be able to turn the game around," he added.

Information from Reuters was used in this report.