A second-half header from Mario Gomez was enough to give Germany all three points against Portugal in their Euro 2012 opener.
Germany dominated the opening period and created the first clear-cut opportunity after just two minutes.
Jerome Boateng found Gomez with a swinging cross and his header forced a good low save from Rui Patricio.
Despite their dominance, Germany almost fell behind in the final minute of the first half as Pepe's fierce strike rattled the underside of the crossbar following a Raul Meireles corner kick.
Portugal improved after the break and Boateng had to make a last-ditch sliding tackle to deny Cristiano Ronaldo when through on goal.
The game soon became subdued as Portugal camped deep inside their own half and denied the group favourites space in behind. However, with 12 minutes remaining, Germany made the breakthrough.
With Gomez, who had been frustrated for most of the game, poised to be replaced by Miroslav Klose, Sami Khedira stood up an excellent cross to the far post and the Bayern Munich target man produced a stunning header back across goal that left Patricio with no chance.
Substitute Varela had a glorious chance to rescue a point for Portugal two minutes from time but he was denied from eight yards by a determined block from Manuel Neuer.
Germany, who are now joint top of Group B, face the Netherlands next in Kharkiv on Wednesday.
