Two late own goals at Old Trafford had seen Thursday’s match at Ramon Sanchez Pizjuan kick off with the tie all square at 2-2.
And another desperate defensive display saw United eliminated, with Youssef En-Nesyri helping himself to a brace after errors from Harry Maguire and David de Gea.
Loic Bade was also on target as Sevilla cruised through courtesy of a 5-2 aggregate success, with Juventus next in the semi-finals.
United had been quick out of the blocks at home last week, but they contributed to their own early downfall this time as Sevilla broke through in the eighth minute.
De Gea fed the ball into Maguire, who was quickly surrounded by three attackers on the edge of the penalty area and saw his attempted pass intercepted by Erik Lamela before En-Nesyri calmly slotted home.
Sevilla continued to pose the greater threat, and the VAR came to United’s rescue five minutes before the break when Marcos Acuna strayed offside before Lucas Ocampos brilliantly fired past De Gea.
It was only a temporary reprieve as Ivan Rakitic’s corner looped up off Bade’s shoulder and over De Gea at the start of the second half.
Ocampos somehow failed to add a third in a goalmouth scramble, allowing United to attempt their own two-goal comeback as Casemiro and Christian Eriksen went close.
But any hopes of a United recovery were ended nine minutes from time when De Gea raced out of his box and failed to make clean contact with a clearance, giving En-Nesyri the opportunity to curl his shot around the stranded goalkeeper.
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