Denmark sit joint-top of Group B with Germany after they both won their opening Euro 2012 fixtures.
Holland were stunned by a first half goal from Michael Krohn-Dehli. The midfielder found space in the box and slotted the ball under keeper Maarten Stekelenburg to give Denmark an early lead.
The Dutch fought back and controlled the game, Arjen Robben looked the most likely to score but could only hit the post.
The pre tournament favourites thought they had a penalty in the 89th minute but referee Damir Skomina waved away the claim even though it seemed to hit Lars Jacobsen's arms.
In the other game a single goal from Mario Gomez was enough to see Germany battle past Portugal to make a winning start to their Euro 2012 campaign.
Portugal's defensive stratergy had frustrated Germany for 72 minutes and Gomez was about to be substituted when he planted Sami Khedira's cross past goalkeeper Rui Patricio.
This sparked the Portugal into life and had a great chance to equalise with minutes remaining but Manuel Neuer denied Silvestre Varela from close range.