It was a dominant display by one of the pre-tournament favourites and it took them just 11 minutes to go in front. Thomas Muller fired home a penalty after Mario Gotze was hauled down by Joao Pereira.
Mats Hummels thumped in a header from Toni Kroos' corner to double the Germans' advantage on 31 minutes.
Five minutes later, Portugal defender Pepe was sent off for a headbutt on Muller - who duly put the result beyond doubt with a close-range finish just before half time.
Ozil had a chance to make it four in the 51st minute when he was played through on goal by Kroos but he shot straight at Rui Patricio before being replaced by Andre Schurrle on 63 minutes.
Muller completed his hat-trick 12 minutes from time with a tap in after Patricio could only parry Schurrle's cross.
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