The Brazilian and the Colombian 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 semi-final, 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.
Spurred on by a capacity crowd in the Estadio Pizjuan, Sevilla were unbowed by their early setback and pushed forward throughout the first half, albeit at times lacking a clear direction as crosses rained down on the Atletico area.
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 the 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. Radamel 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 now 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.
And they continued playing positively after the interval, immediately forcing a save from Courteois who had to get down low to save Alvaro Negredo's low free kick. A delightful pass from the forward then teed up Manuel del Moral, who drove straight at the keeper.
But the action was occurring at both ends; Costa had a great chance to end the game as a contest when Federico Fazio's intervention spun the ball into his path, but the Brazilian uncharacteristically hit wide to spurn his opportunity.
The efforts continued, as Sevilla refused to give up their quest for the final and Atletico failed to close the game down. Falcao went agonisingly 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 offence. 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 their second trophy under the direction of Diego Simeone, after lifting the Europa League title in 2012. Sevilla, meanwhile, miss out on the chance to challenge for the cup they last lifted in 2010.