Mario Gomezscored twice, while the Dutch are heading for a first-round exit.
World Cup finalists Holland will bow out on Sunday unless they beat Portugal in their final game at the Metalist Stadium and hope Germany defeat Denmark the same day in Lviv to give them a chance of reaching the last eight.
After Portugal earlier beat Denmark 3-2 in Group B, Germany now need only a point against the Danes in Lviv the same day to be sure of reaching the last eight at Euro 2012 as group winners.
Having scored the winning header in Germany’s opening 1-0 victory over Portugal, Germany’s Gomez is now the tournament’s early joint top-scorer with Russia’s Alan Dzagoev with three goals after Bastian Schweinsteiger set up both his first-half strikes.
Holland gave themselves a late lifeline when Arsenal striker Robin van Persie pulled a goal back 15 minutes from time, but it was not enough to prevent their second Euro 2012 defeat after Saturday’s shock 1-0 defeat to Denmark.
Scorching temperatures in eastern Ukraine meant the game kicked off with the thermometer showing 29 degrees Celsius (84 degrees Fahrenheit).
Dutch defender Joris Mathijsen was the only change to the team beaten 1-0 by Denmark last Saturday here at Kharkiv’s Metalist Stadium, while the Germans kept the same team which beat Portugal.
A great chance fell to Van Persie after five minutes as a ball over the top got behind the German defence, but the striker could only fire his shot into Neuer’s grateful arms.
Germany replied as Mesut Ozil hit the post from the edge of the penalty area on eight minutes, but the Dutch went back on the attack soon after as Van Persie fired wide this time.
The Germans took the lead thanks to a clever through-ball from Schweinsteiger which beat the Dutch off-side trap and fell to the feet of Gomez, who powered onto the pass and rifled home on 24 minutes.
The pair combined again on 38 minutes when Schweinsteiger’s pass freed Gomez on the right and he fired past Dutch goalkeeper Maarten Stekelenburg on 38 minutes to make it 2-0 to the Germans at the break.
It could have been 3-0 to Joachim Loew‘s Germans as defender Holger Badstuber had headed straight at Stekelenberg before Gomez’s second.
Dutch coach Bert van Marwijk shook up his attack after the break by bringing on Tottenham Hotspur’s Rafael van der Vaart for captain Mark van Bommel and Schalke striker Klaas-Jan Huntelaar for Barcelona’s Ibrahim Afellay.
The Oranje upped the pace and created several chances before Van Persie put them back in the game when he turned Germany defender Mats Hummels to fire an unstoppable shot past Manuel Neuer‘s left hand.
Both sides made changes in the last ten minutes with legs tiring in the stifling heat, as Liverpool’s Dirk Kuyt came on for Bayern’s Arjen Robben, who trudged off with his forlorn face summing up the Oranje’s darkening mood.