Their progress was put under severe pressure late after two goals in the final 10 minutes from the Spanish side, courtesy of Karim Benzema and Sergio Ramos, but Real were unable to find the third goal they needed to go through on away goals.
For much of the match, Dortmund defended stoutly and attacked with purpose, rarely looking overly troubled after a frantic opening 20 minutes—but their passage to the final was not without its drawbacks, as the German side lost playmaker Mario Götze to injury just a few minutes into the match.
Close to the end of the game, they also lost central midfielder Sven Bender to another injury, and he had to be stretchered from the pitch.
Dortmund did ultimately make it through to the final—likely against Bayern Munich with an outside chance of Barcelona making it through, being 4-0 down from the first leg. But that match is just 25 days away, giving their players relatively little time to recover if the knocks prove serious.
Gotze was the first to leave play, seemingly picking up a hamstring injury in the opening stages. There was some discussion on the sidelines between the player and coaching staff, but it quickly became apparent that the soon-to-be Bayern player could not continue.
Generally, a typical grade-two hamstring strain recovery time would be estimated at around two-to-three weeks, though this could be lengthened if the strain is particularly bad or reaches grade three, also known as a complete muscle tear.
Even if Gotze does make a return within the two-to-three week period, he will still have relatively short time before the final itself to make a full recovery to match fitness and is unlikely to be rushed back into domestic action, with the Bundesliga title already wrapped up by Bayern Munich.
His replacement during the second leg against Real Madrid was Kevin Grosskreutz; the more defensive-minded player would likely be the first in line to replace Gotze in the final itself, too.
He certainly doesn't possess the same creative instinct as Gotze, but his hard work and tactical awareness will perhaps let Borussia stifle the threat of either Franck Ribery or Arjen Robben down the Bayern flanks (presuming they don't let their 4-0 lead slip in Barcelona), while the more creative Marco Reus moves central.
Bender is an altogether more difficult injury to assess.
He left the pitch with an apparent Achilles injury, and the same two players suffered calf injuries in the first leg.
The powerful, athletic midfielder holds together the defensive and attacking aspects of the side, knitting together play in deep and final third areas of the pitch, while also putting in a huge shift to keep opposing playmakers under wraps.
Bender would, without a shadow of a doubt, be a huge miss against Bayern, if he were to miss the final. Veteran Sebastian Kehl might be his most probable replacement, leaving Ilkay Gundogan free to roam forward a little more often, but Bender's energy is a potent potential weapon against the same asset of Javi Martinez and Bastian Schweinsteiger.
Regardless of who their eventual opponents are in the final, Borussia Dortmund should go there with no inferiority complex at all.
It was only a year ago that they hammered Bayern in the German Cup final and won the league title, too, while they held the Bavarians to a 1-1 draw in Munich in the Bundesliga earlier this season.
The return clash takes place on May 4; it would perhaps provide a fascinating prequel to the final, if it were not for the fact that both sides might be likely to rest a number of big stars.
Dortmund have three weeks or so to get their team in top shape for the final. With Gotze leaving, Robert Lewandowksi potentially on his way too and a number of other stars at the very least on the shortlist of major clubs all around Europe, this Champions League final could be the biggest and best chance of glory that Dortmund can have during the next decade.
Jurgen Klopp will need his team at full strength, physically and mentally, if he is to pull off a master victory and the crowning achievement of his five-year project at Westfalenstadion.