Bayern Munich striker Gomez scored two delightful goals on 24 and 38 minutes from two pinpoint passes by Bastian Schweinsteiger to add to his winner against Portugal in the opening round of games as Joachim Loew's side threatened to put the match beyond their fierce rivals before half-time.
It was a minor miracle how the Dutch remained in the match until the 73rd minute when Robin van Persie drilled the ball home from distance to give his country hope before they conclude their group matches against Portugal on Sunday evening. Somewhat astonishingly, they are facing an early exit at the Euros only two years after losing to Spain in the World Cup final.
The Netherlands need to beat Portugal by two clear goals and hope Germany overcome Denmark to reach the quarter-finals while Germany must gain at least a point against the Danes to be certain of progress.
Germany will only be denied a spot in the last eight if they lose to Denmark and Portugal overcome the Netherlands. It would then come down to the head-to-heads between the teams to decide who goes through.
With Germany on six points and Denmark and Portugal on three after Portugal's 3-2 win over Denmark earlier in the day, it is worth noting that no team has reached the knockout phase of a European Championship finals after losing their opening two matches.
History is against the Dutch, but at least Van Persie's goal gives them hope of making it through against all the odds. They improved in the second period after being pressed back by a young German side for large swathes of the first period.
As was the case in their 1-0 defeat to Denmark on Saturday, the Dutch came up with a couple of chances early on, but Van Persie screwed an effort wide of goal from Arjen Robben's pass on 10 minutes while the ineffectual Ibrahim Afellay cut the ball across goal for Van Persie but his poor delivery enabled Mats Hummels to make the clearance.
Gomez made them pay when he took one touch from Schweinsteiger's pass before beating Maarten Stekelenburg with the second in the heart of the Dutch area.
Germany should have earned a second goal when Holger Badstuber headed straight at Stekelenburg from Mesut Ozil's cross on 37 minutes.
They did not have to wait long for another uplifting moment as Gomez beat Stekelenburg with a delicious finish from another Schweinsteiger pass as the Dutch defence was cut to shreds on the edge of their own area.
It was the first time at a World Cup or European Championship finals that the Dutch national side had been two goals behind at half-time.
Coach Bert van Marwijk swapped the tiring Mark van Bommel and Afellay for Rafael van der Vaart and Klaas-Jan Huntelaar at half-time, but Hummels almost added a third goal for Germany on 51 minutes when he walloped a couple of efforts at goal only for Stekelenburg to stand tall in repelling his efforts.
The Netherlands were fortunate to be alive in the contest, but gave themselves fresh hope when Van Persie thumped a shot beyond Manuel Neuer from distance after the Germany goalkeeper had denied Van Persie with a diving stop. Wesley Sneijder also lifted an effort wide of goal that might have dipped in on another day or another tournament, but these finals do not look like turning orange.
Despite plenty of huff and puff, the Dutch could not find a way to salvage a draw they were hardly worth with Robben appearing to lose his cool when he hurdled an advertising board on the far side of the pitch after he was replaced by Dirk Kuyt before walking back to the technical area via the side of the park.
It was an act of folly that suggests all is not well in the Dutch squad before they conclude against Portugal on Sunday.