The game was goalless for a long period before Madrid scored twice in the final 10 minutes to set up a frantic finish in the Spanish capital, but the hosts were unable to find a third that would have sent them through on away goals.
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Early on it was Madrid, trailing 4-1 from the opening leg of the semi-final tie, who flew out of the traps. They had three clear openings inside the first quarter of an hour, with Gonzalo Higuain, Cristiano Ronaldo and Mesut Ozil all misfiring.
First Higuain fired straight at Roman Weidenfeller after being slipped in by Ozil before Ronaldo volleyed into the veteran goalkeeper's chest from just a few yards.
Ozil then wasted the best chance of the first half. He was sent clear through on goal with no-one close to him and tried to aim at the far corner and deceive Weidenfeller, but dragged his effort wide of the near post.
Down the other end Dortmund were looking dangerous on the counter and their clearest opportunity came when Sergio Ramos misjudged the flight of a free kick, allowing Robert Lewandowski, who scored four in the first leg, a chance but he volleyed straight at Diego Lopez.
The visitors' lead playmaker Mario Gotze was forced off because of injury in the first half as Dortmund began to weather the Madrid storm and see more of the ball after half an hour.
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Seven minutes after the break Lewandowski squandered a pair of clear-cut chances to put the tie out of Madrid's reach. First he blazed high over the crossbar from Kevin Grosskreutz's pullback and then smashed the underside of the bar from a one-on-one opening.
The hosts continued to plug away but it was Dortmund who looked more dangerous as again they contrived to miss a clear opening. Marco Reus got into the area and squared for Ilkay Gundogan, but his shot from close range was kept out by a sprawling Lopez.
Jose Mourinho's men were struggling to create chances while Dortmund were swift on the counter. Again the German side were denied a fifth goal of the tie when Lewandowski's shot couldn't find a way through a host of Dortmund players.
Real did manage to break the deadlock seven minutes from time when Mesut Ozil's cross was directed high into the net by second-half substitute Karim Benzema.
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Soon after the hosts were within one goal of a miraculous turnaround when Benzema kept the ball in left of the goal and cut it back for Sergio Ramos, who took one touch before lashing into the roof of the net.
Despite goalkeeper Lopez coming up for a late corner, Madrid were unable to find the vital third and Dortmund celebrated wildly upon Howard Webb's final whistle.
BVB are likely to take on fellow German outfit Bayern Munich, who take a 4-0 first-leg lead to Barcelona tomorrow, in the final at Wembley on Saturday, May 25.