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The Portuguese created the first opening in the seventh minute but skipper Christiano Ronaldo's effort was turned fruitless by a good work from the German goalkeeper, Manuel Neuer.
[Read: Germany score 4 goals for third time in 5 WC matches]
[Read: German team vows to win WC for Schumacher]
But Germany drew the first blood at the 11th minute after Joao Pereira's tackle bringing down Mario Gotze led Milorad Mazic, the Serbian referee, gift a penalty to the Germans. Thomas Muller, playing his 50th game, made it 1-0 by putting it past Rui Patricio, the opponent goalkeeper.
Germany scored from a penalty in the regulation time for the 1st time since 1994
Both sides thereafter continued to play an attacking football and the Portuguese came close to draw level at the 26th minute when Nani's target missed the target.
The three-time champions made it 2-0 in the 31st minute when mat Hummels scored from a powerful header. All three goals that he has scored for German have been through headers.
Portugal had the worse waiting for them when Pepe was shown a straight red card for intimidating Muller following an earlier clash.
Germany rubbed salt into Portugal's wounds when Muller scored his second from inside the box in the injury time in the first half.
Muller finished his hat-trick in the 78th minute when he maade full use of a poor clearance by the Portuguese goalkeeper Patricio.
Germany: 1 Neuer (gk), 4 Howedes, 5 Hummels, 6 Khedira, 7 Schurrle, 13 Muller, 16 Lahm (c), 17 Mertesacker, 18 Kroos, 19 Gotze, 20 Boateng
Coach: Joachim Low
Portugal: 12 Rui Patricio (gk), 2 B Alves, 3 Pepe, 13 R Costa, 5 F Coentrao, 7 Ronaldo (c0, 8 J Moutinho, 11 Eder, 16 R Meireles, 17 Nani, 21 J Pereira
Coach: Paulo Bento