Michael Krohn-Dehli gave the Danes the priceless victory to begin the much discussed group of death as a profligate Dutch side started the competition in lackluster style.
There were few signs of what was to come as the match got off to a predictable start with the Dutch dominating possession and pegging Denmark back in their own half. Though not at their best, the Oranje could and probably should have been comfortably ahead at the break.
But instead it was to be a 45 minutes marked by missed chances, with Robin van Persie the central culprit.
The Premier League's golden Boot winner was far from his prolific self as he spurned the game's first clear-cut chance in the opening 10 minutes. Arjen Robben's low cross deflected to the Arsenal man in a great position on his favored left foot, but he could only side-foot the ball the wrong side of the post.
And an arguably even better opportunity came and went later in the first period. Wesley Sneijder laid a simple pass perfectly into Van Persie's path with the goal at his mercy, but the 28-year-old took an uncharacteristically woeful first touch that took him away from goal and allowed his right-footed shot to be blocked by Andersen.
Van Persie was not the only culprit, though, with Arjen Robben also wasteful. Having earlier elected to pass when seemingly in a great position to shoot himself, Robben later elected to go himself, after receiving a poor clearance from the Danish goalkeeper, but could only curl his low shot against the post from the edge of the area.
But by that point the Dutch were already behind as the Danes took full advantage of their opponents profligacy. Michael Krohn-Dehli received the ball on the left of the area and with one clever drop of the shoulder left two Dutch defenders for dead before firing a low left-foot shot past Martin Stekelenburg from the corner of the six-yard box.
The goal rattled the Dutch as they suddenly appeared to have the weight of the world on their shoulders. And Denmark grew in confidence as they began to show up the weakness in the Dutch defense, particularly by doubling up down both flanks.
As the second-half began, Van Persie continued his evening to forget by fluffing his kick when well positioned and then having another shot comfortably held by Andersen. As the pressure increased at the start of the second half, Ibrahim Afellay struck low inches past the post from 20 yards out.
Perhaps frustrated by what he was seeing in front of him, Mark van Bommel strode forward from his deep midfield position and hit a rasping drive that Andersen parried away at full stretch.
The Danes were far from merely hanging on, though, as they continued to try and show enterprise of their own. The goal scorer Krohn-Dehli threatened to add a second as his low drive was turned around his near post by Stekelenburg.
As the 70-minute mark approached and the Dutch remained behind, it was no surprise to see coach Bert van Marwijk bring on both Klaas-Jan Huntelaar and Rafael van der Vaart for Afellay and Nigel de Jong.
With over 40 goals for Schalke last season, Huntelaar looked a good bet to break the deadlock. Instead, he too saw his finishing touch desert him. The strong striker was the recipient of a wondrous pass with the outside of his foot by Sneijder, but in-behind the defense, Huntelaar took the ball too close to Andersen, who did well to block the dinked effort.
The changes failed to inspire the Dutch as they played out the remaining minutes in largely listless fashion, failing to create another genuine opportunity. The closest to a breakthorugh coming with apenalty appeal when the ball hit the hand of defender Lars Jacobsen from close range.
While much of the focus will be on failures of the Dutch, Denmark should earn their fair share of praise for some solid defending and a willingness and ability to cause problems at the other end.
And for the Danes, the victory means the rank outsiders in Group B now have a realistic chance of making the last eight. As for the Netherlands, they now face an unenviable task of needing to get at least a point and possibly more against Germany in on Wednesday.