Having last week built a commanding 4-1 lead over Real Betis, it would have taken a collapse of some magnitude in Seville to see Erik ten Hag’s side give up their place in the final eight.
Juanmi missed a sitter from close range early in the first half that could have changed the script as a packed Benito Villamarin stadium urged on their side to try to wipe out the three-goal deficit.
United goalkeeper David de Gea dived full stretch to deny a long-range effort from 41-year-old Joaquin before Facundo Pellistri struck the post with a close-range strike for the visitors.
De Gea produced an incredible reflex save to keep out a header soon after halftime, but United slowly took control of the game.
Rashford missed a simple chance but atoned immediately, slotting a fine long-range strike inside the left post in the 55th minute.
In Germany, Juventus defeated 10-man Freiburg 2-0 to advance 3-0 on aggregate.
Dusan Vlahovic scored from the penalty spot right on halftime after Freiburg defender Manuel Gudel was sent off for using his hands to deny Adrien Rabiot a goal.
The Italian side controlled the match in the second half and extended their lead five minutes into added time through Federico Chiesa.
In the Netherlands, Feyenoord thrashed Ukraine’s Shakhtar Donetsk 7-1 to progress 8-2 on aggregate as captain Orkun Kokcu and forward Oussama Idrissi each scored twice.
In Turkey, record six-times Europa League winners Sevilla had to dig deep against Fenerbahce, who won the second leg 1-0 thanks to Enner Valencia’s penalty but the Spanish side made the last eight 2-1 on aggregate.
Additional reporting from Reuters