After a tight first half, the crucial breakthrough came moments after the break as Simon Poulsen tried to head a Robin van Persie cross clear only for the ball to strike Agger on the back and fly past a wrong-footed Thomas Sorensen.
At the time the goal was harsh on Denmark after Morten Olsen’s side matched the Dutch in the opening period, but they offered little having fallen behind and can have few complaints about the result.
The Dutch wrapped it up with five minutes left when lively substitute Eljero Elia raced on to a through ball and after his shot struck the post, Dirk Kuyt tapped in the rebound to add gloss to the scoreline.
But in truth, the ninth game of the tournament followed many of its predecessors as both teams struggled for any sort of fluency and neither could find any real attacking momentum in the Johannesburg sunshine.
With World Cup greats Johan Cruyff, Michel Platini and Zinedine Zidane watching on from the stands, it provided another sharp reminder that, Germany apart, so far this tournament has significantly failed to provide the entertaining, creative football many had expected.
Netherlands were many people’s dark horses coming into the competition, but, missing the wing play of the injured Arjen Robben, they struggled to find a way through a dogged Danish defence.
Rafael van der Vaart, Wesley Sneijder and Van Persie all threatened to deliver in the early stages, but the Dutch build-up was too laboured and with Denmark getting men behind the ball they managed to frustrate Bert van Marwijk’s side.
After Van der Vaart had a shot deflected behind and then curled narrowly off target it seemed as though Netherlands had found their feet, but that only prompted the best spell Denmark had in the game.
The Scandinavians burst into life as Nicklas Bendtner headed a gilt-edged chance wide from six yards, Dennis Rommedahl shot straight at Martin Stekelenburg and then Thomas Kahlenberg forced a fine save from the Ajax stopper.
Unfortunately for Denmark, that was as good as it got as, seconds after the restart, Poulsen and Agger’s calamitous moment gave the Dutch an initiative they never looked likely to surrender.
Denmark had no answer to falling behind and the Netherlands began to press for a second they knew would put the result beyond doubt as Van der Vaart brought a sprawling save from an increasingly extended Sorensen.
When the Dutch brought on Elia his pace and directness presented another problem the Danes could not deal with and after Sneijder’s shot was deflected on to the bar, the goal that killed the game arrived soon after.
Elia’s pace took him clear of the static Danish backline and after his shot stuck the post, Kuyt was only hand to wrap up the three points for the jubilant Dutch.
The nearly had another in the closing stages, only for Poulsen to produce a fabulous clearance with an overhead kick, but the damage had already been done and the Netherlands’ World Cup campaign got off to a winning start.
Amiya Sinha is a Special Sports Correspondent of Youth Ki Awaaz and is covering the FIFA 2010 to get you the latest scoop.