Netherlands were made to pay for a raft of missed chances as a first-half goal from Michael Krohn-Dehli handed Denmark a 1-0 win in Kharkiv.
The Dutch had by far the better of the game but were unable to beat the impressive Denmark goalkeeper Stephan Andersen.
The men in orange made the early running but Robin van Persie shot wide and Arjen Robben's dangerous pass was intercepted by a sliding Lars Jacobsen.
The Danes took the lead with a brilliantly-taken goal from Krohn-Dehli on 24 minutes as he 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 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 miscontrolled Wesley Sneijder's pass, allowing Andersen to race out and smother his effort.
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.