No team had ever overturned a first-leg deficit of 3-0 in the Champions League era. It certainly didn't look that way after 37 minutes, when Real Madrid was on the ropes.
Madrid had looked comfortable early on, and Dortmund were cautious through fear of conceding an away goal. Los Blancos kept the ball superbly in one spell, which proved to be their best moment of the match.
After the team made a number of passes on the right, they then switched the play over to the left-hand side. Fabio Coentrao tried to cross the ball, which caught the arm of Lukasz Piszczek, prompting the referee to point to the spot.
It may have seemed a harsh decision, as his back was turned and it was right on the edge of the area. However, Piszczek only had himself to blame. He initially placed both his arms behind him; had he been braver and not twisted when he jumped, it wouldn't have been an issue. He swung an arm out as if to block the ball, but it was his trailing arm that made contact.
Angel Di Maria had the chance to put the tie beyond Dortmund but slipped as he struck the ball, allowing Roman Weidenfeller to palm it away to safety.
The penalty save had given Dortmund a boost and a sense that they could pull off the impossible. All of a sudden they were reinvigorated, pressing and harassing Madrid into mistakes.
Pepe's attempted header back to Iker Casillas was short, and the keeper wasn't able to make up the ground. Marco Reus latched onto the ball and expertly rounded the keeper before putting it through the legs of Sergio Ramos and into the net.
Will Madrid go on to win the Champions League?
Asier Illarramendi then gave the ball away after he was pressed by the Dortmund side. Reus ran at both centre-backs before sliding it through to Lewandowski. The Polish forward tried to put it into the corner, but Casillas got a touch which turned it to the post. Reus followed it up and put Dortmund into a 2-0 lead on the night, which would prove to be the final score.
The opening exchanges of the second half were similar to that of the first. Jurgen Klopp's team knew that there was no rush to get the third and that they couldn't keep up that intensity for the rest of the game.
Henrikh Mkhitaryan could have had at least a hat-trick, as he missed numerous chances throughout the game, including one shot which struck the post.
Real Madrid was clearly second-best, though Dortmund just didn't create enough opportunities and should have scored more. In attack, Madrid didn't possess the cutting edge that we have come to expect from them on the counter.
On the bench, Cristiano Ronaldo was animated but never looked like stripping off and joining the action. They were always going to miss the Portuguese forward, though there was enough talent present to provide a greater threat.
In all the gloom, it was Madrid that advanced to a record 25th Champions League semi-final on a 3-2 aggregate score. The last time they had lost a European match was at the Westfalenstadion last season.
"All games at this stage are very difficult," Carlo Ancelotti told reporters after the match. "We are fortunate to be through to the semi-finals."
You need a lot of luck to win this competition; the wait for La Decima could be over.