Dortmund overturned a 2-1 deficit from their quarter-final first leg against Atletico to win 5-4 on aggregate and will now renew their acquaintance with PSG, who beat Barcelona 6-4 over two legs to book their semi-final berth.
Antoine Griezmann scored twice as Diego Simeone's men moved to within four points of their opponents and pulled five clear of fifth-placed Athletic Bilbao in the race for Champions League qualification.
Antoine Griezmann said Atletico Madrid will have to "suffer" at Borussia Dortmund to reach the Champions League semi-finals.
Atletico Madrid earned a 2-1 Champions League quarterfinal first-leg victory over Borussia Dortmund on Wednesday, surviving a late onslaught from the visitors.
The duo are the underdog sides remaining in this season's quarter-finals, with the other six teams either among the elite
"(Saul) entered the game well and scored a great goal," Simeone told Movistar.
Lewandowski set up goals for Joao Felix and Fermin Lopez either side of striking himself to pull Barcelona second, eight points behind leaders Real Madrid.
Atletico looked dead and buried when Dimarco pushed home Inter's opener.
Atletico Madrid are hoping Antoine Griezmann's injury is nothing more than a sprained ankle after the forward was substituted in their 1-0 defeat by Inter Milan in the first leg of their Champions League last-16 tie, manager Diego Simeone said.
"(Atletico) are taller and they took advantage of that," noted Ancelotti.
Defeat snapped Madrid's 21-match unbeaten run.
"These moments can only be experienced here. All of us who played gave our all," said Brahim Diaz.
Antoine Griezmann became Atletico Madrid's all-time standalone top goalscorer with 174 goals after netting against Real Madrid in the Spanish Super Cup semi-final on Wednesday.
Real Madrid defeated Atletico Madrid 5-3 after extra-time in a pulsating battle in Saudi Arabia to reach the Spanish Super Cup final on Wednesday.
Los Blancos take on Diego Simeone's Atletico on Wednesday in Riyadh in the Spanish Super Cup semi-final, again next week in the Copa del Rey last 16, and also in La Liga in early February.
Atletico Madrid progressed with a 3-1 win at third-tier Lugo after Memphis Depay struck twice, while Real Betis were knocked out in a 1-0 defeat by Alaves.
Girona coach Michel Sanchez insisted his team cannot keep up with La Liga leaders Real Madrid despite their stunning 4-3 win over Atletico Madrid on Wednesday to pull level in first place.
Who would win LaLiga 2023-24?
Griezmann's superb header after 64 minutes split the teams, although visitors Mallorca spurned some good openings in the final stages.