A majestic goal in the 73rd minute from Robin van Persie gave the Dutch a fighting chance in the latter stages but they looked physically spent having been forced to chase the game after falling behind.
Joachim Low's Germany will qualify as group winners if they draw or win their final match against Denmark in Lviv and they are shaping up nicely for a push for a fourth European title.
The only hope the Dutch have of progress is if they beat Portugal in Kharkiv and Germany win, opening up the opportunity to go through on goal difference.
The mathematics may not yet be clear but what was certainly decided in the humid heat of the Metalist Stadium was that the Germans and not the Dutch are the real challengers to Spain's crown.
Even though they may not yet be at their peak Germany were still superior in all departments as the Dutch defence was opened up, their midfield exposed defensively and there was as lack of sharpness in attack.
"It was supposed to be our night but we ended empty-handed as we played poorly," was winger Arjen Robben's frank assessment.
"There is no cohesion between our lines, there are gaps and we are not connecting and then it is very difficult to recover the ball," he added.
The early indications were, however, that the Dutch were going to give Germany's back line a torrid test and skipper Mark van Bommel sent Van Persie clear but he was unable to beat goalkeeper Manuel Neuer.
INSTANT REACTION
That chance triggered an instant reaction from Germany with Mesut Ozil's volley rattling the foot of the post and the ball rolling into Dutch keeper Maarten Stekelenburg's hands.
The Germans grabbed the lead with a goal of genuine quality, the influential Bastian Schweinsteiger threading a pass through the Dutch defence to Gomez, who elegantly turned and fired home with impressive smoothness.
The pair combined again to double the advantage, the Germany striker opting for power as he blasted diagonally across Stekelenburg.
The Dutch left the field showing the worst kind of body language, hands on hips with little communication and only the slightest of glances to each other.
It was clear something had to change radically if the Netherlands were to avoid an even worse fate in the second half.
Coach Bert van Marwijk brought on Bundesliga top scorer Klaas-Jan Huntelaar and midfielder Rafael van der Vaart and they added urgency.
Van Persie tested Neuer with a stinging shot, Wesley Schneider fired just wide with a curling effort and had a fierce drive superbly blocked by a the body of Jerome Boateng.
The Dutch momentum was growing and they got their reward in the 73rd minute in superb style with Van Persie jinking to make room before unleashing a fierce shot from 25 metres.
The prospect of a precious point for the Dutch beckoned but just when they needed to find the extra push they ran out of steam.
"I felt around 65-70 minutes the Dutch were physically drained, very tired," said Low.
"We could have tied it up earlier in the second half. I thought they were tired and we could get a third goal but then it got a bit more exciting with Van Persies's goal," he added.
The Netherlands' problems in their opening defeat by Denmark were limited to a misfiring attack but Van Marwijk said the weaknesses spread much deeper against the Germans.
"In defence and midfield, we gave too much space for them and there was maybe a lack of courage, there was no initiative there," he said.
