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.
Antoine Griezmann struck a hat-trick in a 3-0 win over 10-man Celta Vigo to help Atletico Madrid climb provisionally second, in hot pursuit of their city rivals.
Atletico took an early two-goal lead with Antoine Griezmann and Memphis Depay scoring from close range, while Nahuel Molina extended their lead in the 36th minute in a counter-attack.
Atletico Madrid drew 0-0 at Real Betis in a dour clash.
Atletico Madrid striker Memphis Depay scored with a stunning long-range strike in the second half to help secure a 3-1 home win over promoted Granada in their LaLiga opener on Monday.
Antoine Griezmann shone as Atletico Madrid thrashed Cadiz 5-1 on Wednesday to climb above rivals Real Madrid into second in La Liga.
Atletico Madrid cut the gap on second-place rivals Real Madrid to two points with a 3-1 win over Real Mallorca in La Liga on Wednesday.
Portugal forward Joao Felix said he left Atletico Madrid to join Chelsea on loan because he was struggling to get used to the Spanish side's style of play, adding that coach Diego Simeone's philosophy is not beneficial to every player.
After retiring from playing in 1991 he went on to manage Rayo Vallecano, Racing Santander, Sevilla, Atletico Madrid, Real Zaragoza, Real Valladolid, Malaga and Granada 74.
Real Madrid's Brazil forward Vinicius Jr expects punishment to be handed out by Spanish authorities against hate crimes after a mannequin wearing his No. 20 shirt was hung from a bridge in front of the club's training centre ahead of the Madrid derby.
A dummy dressed in a Vinicius Junior shirt was hung from a bridge near Real Madrid's training ground ahead of the Copa del Rey quarter-final clash against Atletico Madrid on Thursday.