Borussia Dortmund manager Edin Terzic said his side deserved to reach the Champions League semi-finals after a thrilling 4-2 second-leg victory over Atletico Madrid saw the Germans progress 5-4 on aggregate.
Trailing 2-1 from the first leg, goals from Julian Brandt and Ian Maatsen had Dortmund 2-0 up at half time.
Atletico manager Diego Simeone made three changes at the break, including bringing on Angel Correa and his energy told immediately, Mats Hummels conceding a poor own goal before the Argentine netted to put Atletico back ahead in the tie.
But those goals brought a sluggish Dortmund back to life, with Niclas Fullkrug and Marcel Sabitzer each scoring in a three-minute period to send the Bundesliga club through.
"Extremely happy, extremely satisfied and very, very proud of the team and the club," Terzic said. "The atmosphere in the stadium was extraordinarily good.
"There were again two moments that hurt us and could've tipped the balance, but we never lost our belief and stuck with what makes us strong. If you watch both matches, we deservedly reached the semi-finals. It's a big deal for our club."
Former winners Dortmund, fifth in the German Bundesliga and struggling to qualify for next season's Champions League, will next face Paris Saint-Germain for a place in the final at Wembley on June 1.
Dortmund and PSG faced each other in the group stage, with the French champions winning their home match 2-0 and holding the German side to a 1-1 draw Westfalenstadion. However, it was Dortmund who finished top of Group F.
"We've already played against PSG twice. We didn't like the first game in Paris at all," Terzic said. "The second match in Dortmund was very different, close once again, but we managed to get closer to victory than they did. We're a much more solid team than we were in September or even December."
Dortmund should have been level in the tie after three minutes but Sabitzer took an extra touch with the goal beckoning, allowing Atletico to recover.
Buoyed by an 80,000-strong home crowd trying to one-up last week's atmosphere in Madrid, the hosts broke through on 34 minutes, Brandt collecting a Hummels' chip and shooting on the turn, the ball bouncing through Jan Oblak's hands.
The Germans were ahead in the tie just five minutes later, Maatsen threading in from an acute angle after he was given space to run in the Atletico box.
With Simeone sensing his chances of qualifying for the semis for a fourth time as Atletico boss slipping away, he shuffled his deck at half time, making three changes including hooking the ineffective Alvaro Morata for Correa.
Dortmund's wobbles suddenly returned, letting the visitors back into the tie. Hummels turned Mario Hermoso's header into his own net from an Atletico corner under little pressure and with goalkeeper Gregor Kobel waiting to save.
Atletico smelt blood and could have levelled when Correa dragged the ball just wide. The 2022 World Cup winner made up for his miss on 64 minutes when he lashed a loose ball inside the box in off the crossbar, putting Atletico in front on aggregate.
The goal jolted Dortmund back into action and Terzic's men scored twice in three minutes to retake the overall lead.
Fullkrug headed in a Sabitzer cross and the Austrian midfielder then got a goal of his own, shooting through the Atletico defence and into the bottom corner from the edge of the box, grabbing Dortmund a famous victory.
"Champions League semi-finals – it's crazy," Fullkrug said. "It was great to have experienced this game on the pitch for 90 minutes today. The stadium was magical, the atmosphere unbelievable. We on the pitch had a crazy energy because of it."
Atletico were bidding to reach the last four for the first time in seven years, but fell at the quarter-final stage for the third time in five seasons.
"It was tough," Atletico captain Koke told Movistar. "Their goals hurt a lot – the fact that they got them so quickly after each other. We are angry because we wanted to get through. This is football and it can be cruel."
