Thomas Mueller scored the first hat-trick of the 2014 World Cup and was involved in Pepe's red card as Germany breezed past Portugal in Salvador.
The match started brightly, and Germany might have felt some frustration at failing to take a lead when Sami Khedira, receiving a poor clearance from Portugal goalkeeper Rui Patricio, missed the target with the goalmouth gaping.
Joachim Low's men had little cause to dwell on the miss, however, as moments later Joao Pereira pulled down Mario Gotze in the area, and Bayern Munich team-mate Muller stepped up to convert the penalty.
The Germans were two ahead with a little over half an hour played: After Gotze had seen his shot deflected wide, Mats Hummels rose high to power the ensuing Toni Kroos corner into the back of the net.
Portugal's hopes of salvaging a result receded further in the minutes that followed when Pepe was dismissed for violent conduct, having thrown an arm at Muller before stooping to clash heads with his opponent. Germany then tightened their grip when Muller took advantage of a Bruno Alves error in defence to make it 3-0 just before the break.
The 10 men of Portugal struggled to muster a response in the second half as Cristiano Ronaldo, whose fitness had been cause for concern in the build-up to the game, was forced to play the full 90 minutes, with injuries to Hugo Almeida and Fabio Coentrao leading Paulo Bento to use all three substitutes by the 65th minute.
With 15 minutes to play, Portugal saw a penalty appeal turned down when Eder went down in the area, and all hope was extinguished soon afterwards as Muller was able to complete his hat trick with a simple finish after Andre Schurrle's effort was parried into his path.
The goals from Mueller, who signed a new deal at Bayern Munich ahead of Monday's opener, and Hummels mean 11 of the 12 games so far at the World Cup have featured three goals or more.
After the match, Mueller claimed he did not play to get Pepe sent off.