Mueller stroked a 12th-minute spot kick low into the corner of the net and Hummels powered in Toni Kroos's corner from six metres after 32 minutes.
Portugal's misery continued when defender Pepe was sent off after 37 minutes for pushing his head into Mueller as the German sat on the ground following a foul and the forward then lashed home the third goal in stoppage time.
(Reporting by Ed Osmond; Editing by Ken Ferris)
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