The Bayern Munich striker stole all three points for the tournament favorites with a second-half header in a closely-fought encounter that could have gone either way.
Mario Gomez's pinpoint header on 72 minutes sent the beaten 2008 finalist to a crucial three points, and joint-top of Group B with Denmark after their tournament openers.
The match was certainly not one for the purists, with clear-cut chances hard to come by. Both sides gave a disciplined, if not dynamic performance on the field, with the tension becoming unbearable at times in the stands.
After much pre-tournament speculation as to who would spearhead the attack for Germany, coach Joachim Low gave Gomez the nod ahead of Miroslav Klose as the lone striker. The Bayern Munich man looked to repay his manager’s faith early on, sending a guided header from Jerome Boateng’s cross towards goal, which was smothered by Portugal keeper Rui Patricio.
Neither side seemed in any hurry to take control of proceedings, though Cristiano Ronaldo did cause a few hearts to flutter when he flashed a low deflected pass across the face of goal.
With just under a quarter of an hour gone, Germany custodian Manuel Neuer was floored by a dreadful late challenge from Helder Postiga, who was perhaps fortunate to escape his briefing with referee Stephane Lannoy with only a yellow card.
Earlier in Group B’s other fixture, a chance-laden affair saw Denmark stun the Netherlands, but there were no signs of such a spectacle repeating itself as goalmouth action remained elusive.
Germany, despite boasting nearly two-thirds of possession throughout the opening period, could muster nothing more than a few half-chances, with Lukas Podolski guilty of sending a pair of them off target.
Muller lashed across goal after a hurried attack by the Germans, moments before Holger Badstuber was booked for clipping the heels of Nani.
In fact, the best opening of the half fell to Portugal minutes before the break. Pepe attacked a rebound from a corner, but his sidefooted attempt bounced off the crossbar and onto the goal-line without crossing it.
The match remained finely poised as the second half wore on, with Germany just about able to claim the upper hand. On the hour mark, a heavy tackle on Sami Khedira by Fabio Coentrao saw the Real Madrid man receive a yellow card. Boateng soon joined him in the book after manhandling Ronaldo on an attempted Portugal break.
The match needed a spark, and Low seemed set to provide one by readying Klose on the sidelines with 72 minutes gone, with the departure of Gomez appearing imminent.
But no substitution was made at that moment, because after Boateng hit a deflected cross from the right into the box, Gomez climbed above Pepe to head Germany into the lead.
Gomez came within inches of adding another, just failing to get a toe on Muller’s early whipped cross, before belatedly making way for Klose for the last 10 minutes.
That sparked a late surge for Portugal, with Nani twice coming close to bringing it back into the game, one of his efforts being an audacious 35-yard cross that clipped off the woodwork.
Portugal had its best chance of the match two minutes before the end, but Neuer did fantastically well to spread himself and block Nelson Oliveira from point-blank range.
And even later Nani effort was blocked away from goal, with Bruno Alves sending a header over from the resulting corner, as Germany held on to claim victory.
Next up for Germany is a clash against fellow favorites Netherlands, and Portugal squares off against Denmark, with both matches taking place on Wednesday.Follow GOAL.COM USA on