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The home fans made it a very noisy atmosphere in the Spanish capital and they created a host of chances in the first quarter of an hour.
First Gonzalo Higuain was found with an eye-of-the-needle pass by Mesut Ozil but he couldn't beat Roman Weidenfeller from 12 yards. Then it was Cristiano Ronaldo's chance to squander an opening, volleying straight at the Dortmund keeper's chest from only a few yards.
Ozil himself wasted the best opportunity of the early exchanges after being played in with no-one around him and just Weidenfeller to beat. He tried to shape for the far corner and deceive Weidenfeller, but dragged his effort wide of the near post.
As the white shirts continued to pile forward in search of an early goal needed to spark a comeback, Dortmund continued to look dangerous on the counter with the pace of Marco Reus and Lewandowski. The German side did lose one of their stars early on when Mario Gotze was forced off with what appeared to be a hamstring strain.
It remained an end-to-end affair and the next chance fell to Angel di Maria, who struck his shot from the edge of the box against his own teammate and Argentine compatriot Higuain.
As the half entered its final 15 minutes, the yellow-and-black shirts of Dortmund began to see more of the ball, calming the Madrid storm of the early stages.
A 3-0 win for the hosts will guarantee them a place in next month's final.