Sevilla extended their lead with a looping header from defender Loic Bade, before En-Nesyri capitalised on another error, this time from custodian David de Gea, to seal the victory.
Youssef En-Nesyri finished after an error by Harry Maguire to give Spain the lead after eight minutes.
United finished Europe with a whimper, far below their best.
This is the first of a series of potentially season-defining games for United – they play Brighton in the FA Cup semi-finals at Wembley on Sunday and face Tottenham in the Premier League on April 27 – and Erik Ten Hag’s side completely failed this test.
Meanwhile, Sevilla will face Juventus in a two-leg semi-final on May 11 and 18. In their quarter-final, the Italians defeated Sporting 2-1 on aggregate.
United’s nightmare begins with Maguire’s gaffe
United captain Maguire was found wanting for the opener here after helping Sevilla back into the tie with the second own goal in the first leg at Old Trafford.
He received no assistance from his custodian, who played a short pass to him on the edge of the area as three Sevilla players converged in an impressively coordinated press.
However, Maguire should have done better than pass off Erik Lamela, who was only two yards ahead of him. The ball rebounded to En-Nesyri, one of Morocco’s 2022 World Cup stars, who finished past the helpless De Gea.
It set the tone for the first half, in which Sevilla were roared on by a raucous crowd at Ramon Sanchez-Pizjuan Stadium and faced a nervous and uncreative United.
Sevilla may be 13th in La Liga and have spent the majority of the season fighting for relegation, but they appeared reenergized under Jose Luis Mendillibar, their third permanent manager of the season.
After half an hour, a stunning rabona cross from Nemanja Gudelj demonstrated their confidence, while Luis Ocampos appeared to have doubled the lead before the break with a fine finish from the edge of the area, only for a lengthy video assistant referee check to reveal Marcos Acuna had been narrowly offside in the build-up.
Sevilla advances to the final four thanks to a raucous crowd
United, meanwhile, appeared to be lacking in attacking prowess in the absence of suspended Bruno Fernandes and Marcus Rashford, who was on the bench due to a groyne injury. Anthony Martial started up front against the team where he spent part of last season on loan, but was forced off early in the second half due to injury.
Rashford, United’s top scorer this season, was introduced at halftime to replace the ineffective Jadon Sancho, but his side were already two goals down.
Ivan Rakitic’s corner deflected off former Nottingham Forest loanee Bade’s shoulder, looped over De Gea, and went in off the crossbar.
It summed up a terrible night for United all around – Casemiro was uncharacteristically poor in possession, while the injury-enforced absences of Lisandro Martinez and Raphael Varane in defence left gaping chasms of confidence.
However, the worst was saved for last. De Gea rushed out of his goal late in the game to try to clear a long ball, only to slice his attempted half-volley and allow En-Nesyri to slot into an empty goal.
Sevilla have now reached the quarter-finals of all seven Uefa Cup and Europa League competitions in which they have competed, having previously won all six.