The goals were scored by a Simon Busk Poulsen own-goal and Dirk Kuyt late in the game.
Denmark started the match in a bit of a sloppy way, as a weak back pass immediately troubled shot stopper Thomas Sorensen. The keeper managed to clear the ball into safety before Robin van Persie got to the ball though.
The referee awarded Oranje a free kick about 40-yards out in the sixth minute and Wesley Sneijder opted to try his luck from long range. However, the Inter star aimed high and wide and the ball ended up in the stands.
Denmark got the best chance of the match after 27 minutes. Dennis Rommedahl sent in a perfect cross from the right for Nicklas Bendtner and the Arsenal star headed wide from close range.
A counter move by Denmark around the half hour mark caused the Dutch defence some problems. Rommedahl received a switching ball on the right and went past his marker but he fired a ball straight at Stekelenburg.
Stekelenburg again saved the day for Holland minutes later. Bendtner opened up the Dutch defence, sending a through-pass to Kahlenburg. The Wolfsburg midfielder fired in a left-footed shot that was tipped out for a corner.
Van Persie then almost broke the deadlock in the dying seconds of the first half. A lucky rebound fell to the tricky attacker inside the area. Van Persie went by Agger, but slotted wide from close range.
Oranje started the second half brilliantly and opened the score only one minute after the interval. Van Persie went after a long ball down the left wing and collected the pass before sending in a cross to the far post. Denmark defender Simon Poulsen tried to head the ball clear, but his attempt bounced off the back of Daniel Agger past the helpless Denmark goalie to make it 1-0 for the Dutch.
Van Persie got a big chance to double his side's lead in the 52nd minute after an error from Simon Kjaer. Nevertheless, Sorensen rushed off his line to collect the ball before Van Persie got the chance to fire in a shot.
Gronkjaer got past two men after about seventy minutes of play and whipped in a long cross from the left. Going over the head of Rommedahl, the Danes lost the opportunity to equalise though.
Netherlands decided the match five minutes before the final whistle. Sneijder sent Elia clean through on goal with a brilliant through pass. The Hamburg star's shot bounced back off the upright, but Kuyt was alert to tap the rebound home from close range to make it 2-0.
The Dutch came close to making it three only minutes later via Afellay. However, Simon Poulsen cleared the PSV star's shot only inches before the ball crossed the line.