The Netherlands had by far the better of the game on Saturday evening, but they were unable to beat the impressive Stephan Andersen, meaning Krohn-Dehli's first-half strike got the Danes off to a winning start.
The men in Oranje made the early running but Robin van Persie shot wide and Arjen Robben's dangerous square-ball was intercepted by a sliding Lars Jacobsen.
And the Danish then took the lead with a brilliantly-taken goal from Krohn-Dehli, who pounced on a loose ball and surged into the area past Johnny Heitinga, before shooting through Maarten Stekelenburg's legs.
Holland came within inches of levelling when goalkeeper Andersen carelessly kicked the ball straight to Robben but, having advanced to the edge of the box, the winger hit the left upright with his shot.
The Dutch were soon back on the attack and Ibrahim Afellay shot just over before van Persie mis-controlled Wesley Sneijder's pass, allowing Andersen to race out and smother his shot.
And the onslaught continued after the break, but van Persie fell over in the box when played in once again by Sneijder, before Andersen kept out a Mark van Bommel piledriver.
At the other end, Krohn-Dehli almost doubled his tally, drawing a decent save from Stekelenburg with a low shot.
But Andersen was soon pulling off another fine stop, diving at the feet of sub Klaas-Jan Huntelaar, who had been released by a truly brilliant Sneijder pass.
And the Danes survived a vociferous late penalty appeal for handball against Jacobsen to claim a priceless upset win.
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