And it was Michael Krohn-Dehli that provided the lethal finishing that the Dutch inexplicably lacked.
Krohn-Dehli scored against the run of play when he picked up a loose ball close to the penalty area in the 24th minute, left two defenders standing and shot through the legs of Maarten Stekelenburg from a tight angle.
It was something Premier League top scorer Robin van Persie never got close to as he came to symbolize Dutch futility with a couple of bad mistakes. Denmark goalkeeper Stephan Andersen made several clutch saves to secure the most important Danish victory over the Netherlands since the Euro 1992 semifinals.
The Dutch had their best chance of the first half when Andersen gave away the ball to Arjen Robben just outside the area in the 36th minute, but the Bayern Munich winger curled his left-footer onto the far post and out of danger.
It came to symbolize the sticky night in eastern Ukraine and leaves the World Cup runners-up with two clutch games against top-10 ranked teams, Germany and Portugal.
Late in the match, a penalty appeal for handball was denied when the Dutch were running out of time as Lars Jacobsen appeared to touch the ball with his upper arm in the box.
Denmark, seen as outsider in the toughest group of the championship, can already take a huge step to the quarterfinals by beating Portugal in their second game.
From the start, the tactics of the match were laid out for all 39,232 fans at the Metalist Stadium. The Dutch started with furious attacking and the Danes counted on a solid attack and a dose of luck to keep out of danger.
The creative skills of Robben, Van Persie and Ibrahim Afellay created plenty of chances, but finishing was off and Andersen would not budge.
With one lethal counter, Krohn-Dehli showed some of Europe's best players how it should be done with his well-taken strike.
The Netherlands came into the tournament without key defender Joris Mathijsen and a questionable left defensive flank. Ron Vlaar and Jetro Willems confirmed the assumptions as the back line did not look at ease when the Danes came pushing forward around the half-hour mark.
Netherlands coach Bert van Marwijk even had to come to the sideline to shout and wave his players forward. And on a difficult day, luck was not with the Dutch either, when Robben's shot bounced free.
Van Marwijk's decision to pick Van Persie over Bundesliga top scorer Klaas-Jan Huntelaar came into sharp focus. Two minutes from halftime, Wesley Sneijder set up the Arsenal striker in the center with only the goalkeeper to beat.
Uncharacteristically, Van Persie had a bad first touch and was forced too wide and shot at the goalkeeper instead of scoring an easy goal.
Early in the second half, too, he inexplicably mis-stepped on another great chance for goal as the Dutch pushed forward from the second half whistle. They forced Andersen into two fine saves on a half dozen occasions.
The thousands of orange-clad fans filled the air with shouts of ''Holland, Holland,'' but to no avail.
The Danes didn't fully lock themselves up but showed poise by patiently pushing forward again. Still, the Dutch kept piling up the misses and Van Marwijk brought in both Huntelaar and attacking midfielder Rafael van der Vaart for defensive midfielder Nigel de Jong with 20 minutes to go.