The Spanish champions almost produced a comeback for the ages after their 4-0 first leg defeat in early February, but fell just short at Camp Nou.
Youngster Marc Bernal netted twice for the record 32-time winners and Raphinha scored a penalty as Barcelona tried in vain to claw back Diego Simeone’s side’s lead.
Atletico, who clung on desperately in the final stages, returned to the final for the first time since 2013.
They will face Real Sociedad or Athletic Bilbao, who meet on Wednesday in the second semi-final second leg.
“We knew it would be a tricky game, to come back from 4-0 down is not easy. But I’m proud of the team, we gave everything,” Raphinha told Movistar.
“We are disappointed because we wanted to be in the final, and I think we deserved it from the game we played, but we have to respect Atletico too, a great team and they defended what they had and did well.”
Atletico goalkeeper Juan Musso admitted his team were up against the wall but was delighted to reach the final.
“We are dreaming of winning the cup. Maybe it wasn’t our best game, we were better in the first leg,” Musso said.
“We showed what we were made of in the final 15 minutes, it was all in their favour, their pitch, their fans, they needed just one more goal, but the team suffered through it.”
Barcelona came out flying and Fermin Lopez’s long-range effort just over the bar set the tone, as Hansi Flick’s side threw everything they had at a potential comeback.
They were dealt an early setback when Jules Kounde went off injured in the opening stages. Antoine Griezmann came close against his former side as Atletico threatened on the counter-attack.
Ferran Torres fired wide and had a shot saved low at the near post by Musso before Barcelona took the lead.
Teenage star Lamine Yamal drilled across the face of goal for Bernal to finish from close range, with one 18-year-old setting up another.
Ademola Lookman headed narrowly off-target for Atletico and came to rue the miss as Barca doubled their advantage before the interval.
Spain midfielder Pedri was tripped in the box by Marc Pubill and Raphinha sent Musso the wrong way from the spot. (AFP)
Edited by Cecil Wong
