Michael Krohn-Dehli's 24th minute strike consigned the Netherlands to a shock 1-0 defeat to Denmark in their opening Group B encounter.
In the day's other game, Mario Gomez repaid Joachim Low's faith to start him in place of Miroslav Klose, by scoring Germany's lone goal in their win against Portugal.
In the opening match, the Dutch, as expected, dominated the proceedings, but wayward finishing from their forward line, saw them fail to find the back of the net. Denmark, who looked dangerous whenever they went forward, will be delighted to take full points in a group, where they were expected to finish last.
Krohn-Dehli smashed an angled drive past Dutch goalkeeper Marten Stekelenburg to hand Denmark the win. The Dutch were guilty of missing several chances, with the likes of Robin Van Persie and Arjen Robben failing to work the goalkeeper enough.
The Dutch could have won a penalty in the dying minutes after the ball seemed to strike Lars Jacobsen's hand twice in the penalty box, but referee Damir Skomina waved play on, to the frustration of the World Cup runners-up.
After the match, Dutch coach Van Marwijk, rued his side's missed chances. "There were maybe four, five, six players who had a lot of chances. And the referee had also a chance to give us a penalty.
"I'm not looking for excuses. I'm just trying to give answers to the questions.
"The players really wanted to do something with all the chances but the ball just didn't want to go in.
"We were really determined, but you have to score that goal, of course. When there's a penalty that doesn't go in your favour, that's unfortunate but that's part of the game.
"We just have to beat Germany. That's not going to be easy but that's the goal now and everyone knows that."
Later, Gomez's header in the 72nd minute was enough to give Germany 3 points and help them take control in the Group of Death. In a cagey game, Germany were left frustrated for much of the 90. However, with Gomez on the verge of being substituted for Klose, the Bayern Munich striker brilliantly guided a cross from Sami Khedira to the far corner, sending the German fans into delirium.
Portugal, who had hardly seen the ball before the goal, finally woke up and created a few chances in the final moments, but Germany held on.
"This is the start of the European Championship," Low said after the game. "It's like a Formula One race but without a warm-up. You have to be ready straight away because every team is incredibly strong. There is no team like in the World Cup where you can acclimatise yourself. Portugal were right there straight away.
"You could feel both teams were quite tense, especially after the Holland-Denmark result. Both teams knew the team that lost would have a lot to do in the next game -- kind of like a knockout situation.
"We were much more compact, disciplined in defense, as was the case in the last few weeks. We could have attacked a bit better, but we will do that. The main thing is that we won and we've got these three points."
