The ball was nearly in the net at the other end just a minute later after Rui Patricio's scuffed clearance went straight to Sami Khedira, though the German midfielder could only shoot off target from all of 40 yards.
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Both teams continued to show plenty of attacking intent throughout the remainder of the half, and Portugal came close to finding an equaliser on 26 minutes when Nani blasted the ball narrowly over the crossbar from 20 yards.
However, it was the Germans who doubled their lead with 31 minutes played thanks to a powerful header from Mats Hummels following a corner.
A disastrous half for Portugal was made worse on 36 minutes when Pepe was shown a straight red card after a confrontation with Muller.
The defender took exception to what he believed was an over-reaction from the forward following an earlier clash, but the referee had no option other than to send him off after he went into his opponent with his head.
Germany then extended their advantage further on the stroke of half time as Muller was picked out by Gotze before firing home from inside the box.