Ten-man Barcelona completed the Spanish league and cup double as two goals in extra time clinched the Copa del Rey.
Luis Enrique’s side claimed the trophy for the 28th time despite having Javier Mascherano sent off in the first half.
Jordi Alba and Neymar scored for Barcelona, who can boast back-to-back doubles after winning La Liga.
Sevilla had Ever Banega dismissed in stoppage time at the end of 90 minutes and Daniel Carrico at the end of extra time as they finished with nine men.
Mascherano was given a straight red card in the 36th minute for dragging down Kevin Gameiro by his shirt as the Frenchman raced towards goal.
Five minutes into the second half, Barcelona defender Gerard Pique produced a vital deflection to divert a long-range effort from Banega onto the post and, after an end-to-end second half, Banega was sent off in stoppage time for chopping down Neymar on the edge of the area.
Barcelona broke the deadlock seven minutes into extra time when Alba sprinted to meet Lionel Messi’s fine crossfield pass and finished first time across goalkeeper Sergio Rico and into the bottom corner.
Carrico was dismissed in stoppage time at the end of extra time when he received a yellow card for a foul on Messi and another for his angry protest.
Messi then fed Neymar for the Brazilian to add a second with a confident finish.