Michael Krohn-Dehli's expertly taken first-half strike earned Denmark a shock win against a Netherlands side who missed a host of chances.
Krohn-Dehli drifted away from two defenders to fire home the winner.
But the Dutch wasted numerous efforts with Arjen Robben and Robin van Persie the main culprits.
"It happened to Robin van Persie at the 2010 World Cup. He maybe takes on too much responsibility. He should be flying after a season like he has had [with Arsenal]. He's not relaxed enough. When he plays for Arsenal it's a different Van Persie."
Robben came closest when he shot against the post and the Danes survived a late handball appeal against Lars Jacobsen to hold on for victory.
Denmark coach Morten Olsen's pre-match warning that the Netherlands were simply better than his side could easily have been dismissed as mind games.
But for long spells the reality backed up Olsen's fears and the Dutch dominated.
They combined their undoubted guile, creativity, pace and attacking quality with midfield grit and organisation.
Van Persie and Robben provided the cutting edge, and they had numerous chances to put Bert van Marwijk's side ahead before the Danes took the lead.
Van Persie, who scored 36 goals for Arsenal last season, sidefooted the first opening wide after a good early Robben run and Van Persie teed up a headed chance for Wesley Sneijder.
Robben and Van Persie then combined brilliantly on the right only for the former Bayern Munich winger to fail to pick out one of two team-mates in the middle.
Sneijder also sent a header wide and a Dutch goal looked inevitable.
But the Danes remained resolute in defence - largely thanks to a spirited display by captain Daniel Agger - and they went ahead with their first meaningful attack.
Krohn-Dehli took advantage of a lucky bounce of the ball after a battling run on the left flank by Simon Poulsen, dummied two Dutch defenders and shot low through goalkeeper Maarten Stekelenburg's legs.
Niki Zimling did have a chance to double the lead soon after, but failed to properly connect with a difficult volleyed effort.
That was, however, a brief interlude to a series of Dutch attacks.
Robben curled an effort against the foot of the post from the edge of the box after being gifted the ball by an abysmal clearance from keeper Stephan Andersen.
And Netherlands started the second period in blistering fashion and could have had four goals within 10 minutes
Robben shot over after cutting in from the left, and Van Persie miskicked dreadfully when in a good position and was also unlucky with another low effort.
Defender makes history
Netherlands left-back Jetro Williams' inclusion means he is the youngest player to feature in the European Championship finals at just 18 years and 71 days old. Whose record did he eclipse? Enzo Scifo, the brilliant Belgian midfielder who was 18 years and 115 days when he faced Yugoslavia in 1984.
Mark van Bommel also went close with a fizzing 25-yard strike that drew a fine save from Andersen.
At the other end, goalscorer Krohn-Dehli's 20-yard strike brought a fine save from Stekelenburg.
And, although the Dutch started to look increasingly frustrated, they still created chances.
Substitute Klaas-Jan Huntelaar - left out of the starting line-up despite scoring 12 goals in qualifying - went through on goal but was denied by some alert and brave goalkeeping and Huntelaar also had a decent claim for a penalty dismissed.
Defender Jacobsen handled the ball while under pressure from Huntelaar, but the referee waved away Dutch appeals for a penalty.
The Danes held firm and now have a great opportunity to progress to the quarter-finals, while the Dutch - runners-up at the last World Cup - must win at least one of their remaining two fixtures, against either Germany or Portugal, to have any hope.