World Cup finalists Holland will bow out on Sunday unless they beat Portugal in their final game here 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 three goals after Bastian Schweinsteiger set up both his first-half strikes.
Holland earned a late lifeline when Arsenal striker Robin van Persie pulled a goal back 15 minutes from time yesterday, but it was not enough to prevent their second Euro 2012 defeat after Saturday's shock 1-0 defeat to Denmark.
"It was very tight right up until the end and was nerve-wracking for us," admitted goal-scorer Gomez.
"We have to remain realistic, we have taken six points against two top-class teams, but we want more.
"I'm very happy to have scored two goals to help the team, it is important that the right players and the coach are behind me. "There is still a long way to the final."
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 by Denmark here again in Kharkiv, while the Germans kept the same team which beat Portugal.