Real finished with a head of steam to take the second leg 2-0 at the Bernabeu, but they fell short by one goal and it was Dortmund dancing for joy at the end.
The 4-1 deficit from the first leg proved too great, although one more goal to take the aggregate score to 4-4 would have been enough to take Real through due to their solitary away goal.
Both sides squandered clear-cut chances throughout the game, with Real dominating, but the deadlock wasn’t broken until the 82nd minute when Karim Benzema scored from inside the box.
Sergio Ramos scored moments later after some tight passing.
Ramos went close again before the end, while Cristiano Ronaldo tried his luck at milking a late penalty from English referee Howard Webb who was having none of it.
Bayern Munich go to the Nou Camp in Barcelona tonight with a massive buffer after their 4-0 win last week at home.
The German side’s boss Jupp Heynckes has insisted he will start with his strongest 11, even though six of his players are one booking from missing the final against Dortmund, assuming they progress.
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