The German side took a 4-1 advantage into the return leg after a stunning performance at the Westfalenstadion last week and it paid off even though they conceded twice late at the death.
Goals in the final ten minutes from Karim Benzema and Sergio Ramos gave Dortmund a scare but they eventually saw it out at the Santiago Bernabeu to move through to the decider to be played at London's Wembley Stadium on May 25.
The opening goal came in the 83rd minute when Mesut Ozil's inviting cross was finished at close range by Benzema, five minutes before Ramos grabbed a second, rifling into the roof from a Bernzema pass.
Real started in aggressive style, creating some early chances, but Dortmund were able to quell them for most of the 90 minutes before some attacking waves from Jose Mourinho's men broke them down.
In the end, however, it was Juergen Klopp who reigned supreme and his side will now await either Barcelona or Bayern Munich who battle it out at the Nou Camp on Wednesday following Bayern's 4-0 triumph at home last week.
2012/13 UEFA Champions League semi-final - second leg
Santiago Bernabeu, Madrid - 79,429