Marcel Sabitzer scored late and set up two goals to send Borussia Dortmund into the Champions League semifinals with a helter-skelter 4-2 win over Atlético Madrid on Tuesday.

After losing the first leg of their quarterfinal 2-1 in Madrid, Dortmund had to come from behind twice over two legs to advance 5-4 on aggregate.

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Julian Brandt opened the scoring to level the tie before Sabitzer set up Ian Maatsen to give Dortmund a 2-0 lead on the night.

Atlético coach Diego Simeone responded with three changes at the break and they all paid off. A Mats Hummels own goal and goal from substitute Joaquín Correa put the Spanish side back in front on aggregate.

Then Sabitzer set up Niclas Füllkrug in the 71st minute for the Germany forward's first goal after nine scoreless games, and Sabitzer scored himself three minutes later to send Dortmund into the last four.

"That was a rollercoaster, a really great evening," Dortmund chief executive Hans-Joachim Watzke said. "It's not always like that for Borussia Dortmund. The last time we were in the semifinals was in 2013. This is a great day for all Borussen."

Dortmund will face Paris Saint-Germain again in the semifinals. PSG progressed to the final four with a 4-1 win at Barcelona. And Dortmund coach Edin Terzic feels his side, who won the Champions League in 1997, are now better prepared to face the French champions, after the Germans lost away and drew at home in the group stage.

"Our first game against them wasn't good. In the second game, we adjusted to them better and were closer to victory. I think we're a better team today than we were against them in the group stage," Terzic said following the win over Atletico.

The final will be played June 1 in London, where Dortmund lost the 2013 final 2-1 to bitter rival Bayern Munich.

Tuesday's win stretched Dortmund's unbeaten run at home in the Champions League to 10 games.

"We were close to tying the game, but they were superior, and when a team is superior they should be congratulated," Simeone said.

Atlético needed goalkeeper Jan Oblak at his best. He denied Brandt, then Karim Adeyemi, before Brandt finally made the breakthrough in the 34th, firing a powerful shot in off Oblak's leg from a difficult angle after eluding former teammate Axel Witsel.

Sabitzer then combined with Maatsen, who surged past two defenders and fired the ball inside the far post in the 39th. It was the Dutch defender's first Champions League goal.

But Atlético only needed four minutes after the break to level the tie when Hummels' attempted clearance of Mario Hermoso's header ended in his own net.

Correa should have scored shortly afterward when he nudged the ball wide. Simeone - dressed sharply in a black suit - flopped to the ground in frustration.

Correa made no mistake in the 64th when he fired in a rebound after his first attempt was blocked.

It put the visitors back in front, but Sabitzer was involved in both goals as Dortmund struck twice in three minutes to send the home fans wild.

"It was a crazy game for the fans and for us. A great game for us, for our fans and for all football fans around the world," Brandt said after receiving his man-of-the-match award.

"It's going to be very serious now against Paris. We played well against them at home in the group stage, but not well away. We want to do better now and, of course, reach the final."

For striker Niclas Fullkrug, who also got on the scoresheet, the Champions League semifinals will be a new experience.

"I've never played at this level before and I'm very proud to be in the semifinals of the Champions League with my team," Fullkrug said. "Things will certainly be different against Paris than in the group stage."

Information from Reuters and The Associated Press was used in this story.