Borussia Dortmund fought back to beat Atletico Madrid 4-2 in their quarter-final second leg on Tuesday, securing a 5-4 aggregate victory and a first Champions League semi-final since 2013.

Trailing 2-1 from the first leg, goals from Julian Brandt and Ian Maatsen had Dortmund 2-0 up at half-time.

Visiting coach Diego Simeone made three changes at half-time 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 Fuellkrug and Marcel Sabitzer each scoring in a three-minute period to send the Bundesliga club through.

Former winners Dortmund, fifth in the German top flight 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.

The home side should have been level in the tie after three minutes but Sabitzer took an extra touch with the goal beckoning, allowing Atletico to cover.

Just moments later, Atletico had a major chance of their own, as Alvaro Morata raced through one-on-one with the goalkeeper but chipped the ball well wide of the post.

Buoyed by an 80,000-strong home crowd trying to one-up last week's atmosphere in the Spanish capital, Dortmund pushed and prodded, with Karim Adeyemi blasting straight at Jan Oblak.

Dortmund broke through after 34 minutes, Brandt collecting a Hummels chip and shooting on the turn, the ball bouncing through Oblak's hands.

The home side 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 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 World Cup winner made up for his miss on 64 minutes when he cut through a penalty area crowded with yellow shirts and smacked the ball in, sending Atletico in front on aggregate.

The goal jolted Dortmund back into action and Edin Terzic's men scored twice in three minutes to retake the overall lead.

Fuellkrug 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.