The game never lived up to expectations and looked to be heading for a goalless stalemate, particularly after the Germans spurned a number of good chances.
The importance of not giving up showed its worth yet again in the 72nd minute when a deep right-wing cross from Sami Khedira flicked off a Portuguese defender and Gomez for once found himself free to nod home the winner.
"We started in this tournament with music but we have to improve... we'll have to attack with more focus but I'm confident we'll succeed in doing that," said German coach Joachim Low, who at one point in the first half jumped from the bench to berate his players.
Germany are now favorites to qualify from a tough group, especially after the fancied Dutch team surprisingly lost 1-0 to Denmark in the earlier game.
Portugal hit the bar twice but otherwise rarely threatened and coach Paolo Bento will surely be worried by the ease with which the Germans stifled Portugal's rocket-heeled wingers Cristiano Ronaldo and Nani.
Both had had frustrating evenings as a disappointing Portugal, who have now won just one of their last seven games, only looked dangerous in the last 10 minutes.
"I am sad about the result because we had a stronger first half... we have to concentrate in second game and we have to win it," said Bento.
Germany dominated yet almost went behind when Portuguese defender Pepe hit a close range shot against the crossbar late in the first half. The ball bounced down onto the line and was cleared.
Gomez, preferred up front to Miroslav Klose, made no mistake when he evaded the diligent Portuguese defense and headed home his 23rd international goal.
"I had a good feeling from the start here and I wanted to give something back for the trust [the coach put on me]," he told German television.
"It was clear when Miro [Klose] was on the bench and would come in for me at the end for a few minutes. It's hard to head in a ball when you're taking a step backwards but I think the ball was deflected a bit so it worked out."
In a flat first half German fans caused almost as much excitement off the pitch, throwing what appeared to be rolled up pieces of paper at the Portuguese players on several occasions in the first half.
Authorities warned supporters three times that such behavior could force the match to be abandoned.
Germany twice tested Rui Patricio in the first 10 minutes through a header from Gomez and a Lukas Podolski shot that the keeper grabbed at the second attempt. Podolski later skied an effort well over the bar from just outside the box.
Portugal, who have scored just once in their last four matches, did little with Helder Postiga alone up front, supported by widemen Ronaldo and Nani.
They only came to life late on when substitute Silvestre Varela hit the bar with a cross from the right and then saw a close range effort well saved by German keeper Manuel Neuer.
Although Bento said he was happy with Ronaldo's performance, the Real Madrid forward did not impress and cemented his reputation for producing memorable performances at club level and falling short for Portugal.
