Diego Costa and Radamel Falcao stole the show in the Pizjuan, meaning that the Colchoneros will meet Real Madrid in a dream final for fans of the capital giants
Diego Simeone's men again scored two in Andalucia thanks to strikes from Diego Costa and Radamel Falcao in the first half, while Jesus Navas and Ivan Rakitic's goals proved to be insufficient for the disappointed home support.
Having witnessed the Colchoneros take a narrow lead from the opening clash of the semifinal, fans of both Sevilla and Atletico were expecting a gripping clash as their men fought for a place in the Copa del Rey showpiece. Right from the outset, it was clear that they were not to be disappointed as Atleti raced into the lead.
Receiving the ball on the edge of the box, Diego Costa did fantastically well to simultaneously gain control while holding off the challenge of Alberto Botia. Turning the defender expertly, Costa was equally lethal in driving his shot low past the dive of Beto to open the scoring, earning the Brazilian his seventh goal of the cup campaign with just six minutes played.
Gary Medel had one of the Rojiblanco's best early efforts; having seen Jesus Navas slalom his way down the right flank and float in a cross. The Chilean was left with an almost empty net when Thibaut Courteois misjudged the flight of the ball, but nodded wide to squander the opportunity.
Atletico's retribution was swift. Falcao started his side on the offensive, taking the ball on the counter and opening up with a long pass to find strike partner Diego Costa. Costa flew down the left wing, and upon reaching the byline had the easy task of finding the Colombian in the penalty area, who barely broke stride as he converted coolly to complete the move.
Sevilla looked sunk 4-1 down on aggregate, but there was to be one beam of light in the first half; Navas turned in a delightful looping shot from the edge of the area as the match approached the midway stage, giving his side the slightest of lifelines for the remaining 45 minutes.
Sevilla continued playing positively after the interval, immediately forcing a save from Courteois who had to get down low to save Alvaro Negredo's free kick. A delightful pass from the forward then teed up Manuel del Moral, who drove straight at the keeper.
The efforts continued, as Sevilla refused to give up its quest for the final and Atletico failed to close the game down. Falcao went agonizingly close with a header that should really have hit the target, while minutes later it was Negredo's turn to take his head into his hands after seeing his own chance go wide.
But whatever opportunity Sevilla had of getting back into the game, with 15 minutes left it evaporated when Medel was expelled from the field for a second bookable offense. The ex-Boca Juniors and Universidad Catolica star had to be dragged away from the action as he was incensed by the decision.
And the Chilean's exit was the final straw for the hosts as they went out of the Copa del Rey in the penultimate stage, Ivan Rakitic's late strike too little to change the course of proceedings.
Atletico will now have the chance to win its second trophy under the direction of Diego Simeone, after lifting the Europa League title in 2012. Sevilla, meanwhile, misses out on the chance to challenge for the cup it last lifted in 2010.