The Andalusians beat Barca 2-1 at the Nou Camp in the first leg and goalkeeper and captain Andres Palop was the hero in the return, producing a string of superb saves to deny Pep Guardiola and his players a repeat of their 2009 triumph.
Barca can no longer match last year's feat of winning an unprecedented six titles and it was the first time they have been eliminated from a competition since April 2008 when they lost to Manchester United in the Champions League semis.
Sevilla, the 2007 winners, will play La Liga rivals Deportivo La Coruna in the quarter-finals after the Galicians came from two down at home to draw 2-2 with Valencia for a 4-3 aggregate victory.
Getafe overturned a 2-1 first-leg deficit to come through 6-3 against visiting Malaga, and Osasuna progressed on away goals against second-division leaders Hercules to set up a last-eight tie against Racing Santander.
Racing were held to a 0-0 home draw by lowly third-tier Alcorcon, conquerors of Real Madrid in the last round, but advanced 3-2 on aggregate.
EARLY PRESSURE
Barca came under early pressure on a sodden pitch at the Sanchez Pizjuan and Ndri Romaric tested goalkeeper Jose Manuel Pinto with a firm downward header after three minutes.
Barca found it hard to keep the ball on the slippery surface but Zlatan Ibrahimovic had a chance just before the half hour which he sliced well wide.
The visitors stepped up the pressure at the start of the second half and Palop saved superbly from an Ibrahimovic header and denied Lionel Messi and Thierry Henry with equally impressive stops.
A fine strike from Spain midfielder Xavi in the 64th minute gave Barca hope and the rampant Messi fired a shot against a post in the 69th.
Guardiola brought on forwards Bojan Krkic and Pedro with five minutes of regular time remaining and Barca pressed for the goal that would send them through but Sevilla held firm, with Palop producing another brilliant save from Messi at the death.
