Sevilla, who trailed 2-1 from the opening match, looked to be heading out of the competition when Diego Costa and Radamel Falcao gave their opponents the lead.
Jesus Navas gave the home side hope before the interval, but a red card for Gary Medel in the second half complicated matters further.
Ivan Rakitic's eventual equaliser came too late for Sevilla, who also saw Geoffrey Kondogbia sent off in the dying seconds to cap a miserable evening. Atletico will now play city rivals Real Madrid in the final.
With the rain lashing down at Estadio Ramon Sanchez Pizjuan, Atletico were in front after just six minutes thanks to Costa, who held off the challenges of two defenders before drilling home from 10 yards out.
It took Sevilla 20 minutes to create their first meaningful chance, with Navas looping a ball to the far post where Medel headed narrowly wide.
And the miss came back to haunt them nine minutes later when Atletico scored again. Costa was at the heart of the move, whipping in a cross from the left to Falcao, who hit a first-time shot into the bottom right corner.
This time Sevilla managed to respond and 10 minutes later Navas had added his name to the scoresheet, smashing home an angled shot off the right post following a cross from Jose Antonio Reyes.
That sparked a spell of pressure from the home side and they should have been level three minutes before the interval but Rakitic failed to finish Medel's assist and directed a header wide from an unmarked position.
Sevilla pushed again in the second half but Alvaro Negredo was denied after 53 minutes by a parried save from visiting goalkeeper Thibaut Courtois.
Moments later Costa should have put the match beyond doubt for Atletico but he failed to make the most of his chance from a few yards out and, under pressure from a defender, poked a shot wide of the left post.
Sevilla's evening took a further turn for the worse after 76 minutes when Medel was shown first a yellow card and then a red for dissent.
Atletico failed to finish off their opponents though, and Sevilla grabbed a late if immaterial equaliser in stoppage time when Kondogbia's through ball found Rakitic, who finished right footed into the bottom corner.
The match then finished on a sour note for Kondogbia, who saw a straight red in the final seconds for bringing his foot down on Costa.
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