Danish midfielder Michael Krohn-Dehli got the winner in the first half but the outcome was determined by the failure of the Dutch to turn chances into goals, leaving Bert van Marwijk's team facing a tough challenge to get out of Group B.
Just as Chelsea proved with their unlikely Champions League triumphs over Barcelona and Bayern Munich to lift the trophy, the Danes showed that a superior team can be defeated by stout defending, hard work and 90 minutes of concentration.
"The most important thing is that we trusted our own way of playing football, that is so vital, particularly against a quality team like the Dutch," said Denmark coach Morten Olsen.
The Danes were disciplined and patient, as Olsen had asked them to be, but it was the Netherlands' poor finishing that really decided the outcome of the contest.
"We did a lot of good work but that's the game - we were the best team, but you have to score to win," said Van Marwijk.
Statistics can be misleading but this time the numbers highlighted the key to the game - Netherlands had 28 attempts on goal but 20 of those failed to trouble keeper Stephan Andersen.
The Danes, in contrast, mustered just eight efforts but all were on target, including Krohn-Dehli's clinical strike through keeper Maarten Stekelenburg's legs in the 24th minute.
Left-back Simon Poulsen raced down the wing and superbly pulled the ball back into the path of the midfielder, who skipped past John Heitinga and fired home.
The goal came after Netherlands, who started Jetro Willems at left-back making him the youngest player to take the field in a European Championship match at 18 years and 71 days old, had totally dominated the opening period, taking full advantage of some disjointed and ineffective play from the Danes.
Robin van Persie, English Premier League top scorer last season but the main culprit in terms of finishing on Saturday, set the tone in the seventh minute when Arjen Robben found him with an incisive pass but the striker screwed his shot wide.
Van Persie then produced a trademark turn to create space for a shot in the 23rd minute but his off-target effort was far from his usual high standards.
The goal did little to change the flow of the game but, apart from when Robben hit the post after collecting a poor clearance from Andersen, the Dutch attacks ended in wasteful off-target efforts.
In contrast, Krohn-Dehli threatened again just before the break with another low shot - a reminder to the Dutch that they could not throw caution totally to the wind in the second half.
They had another four good chances in the opening 10 minutes after the break but their frustration was encapsulated by Van Persie losing his balance and falling over after being put through by the enterprising Wesley Schneider.
Again, Krohn-Dehli responded with a sharp shot on target and it was no surprise when in the 71st minute Netherlands coach Van Marwijk introduced striker Klaas-Jan Huntelaar, the top scorer in both Euro qualifying and last season's Bundesliga.
But the increased numbers up front did nothing to address the lack of composure and, having forced the pace for so long, the Dutch not surprisingly ran out of steam.
Van Marwijk said there was not a lot, in terms of strategy, he could have done to help his team preserve their energy better for a late push.
"It's not an excuse, in a game like that you lose less energy defending and playing in closed spaces, as the Danes did," he said. "But it's hard to tell your team to defend more when you are losing 1-0 and
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