The Red Devils secured their spot in the last-eight, recovering from an early setback to win 4-1 on the night and 5-2 on aggregate.
Real Sociedad's Mikel Oyarzabal converted a penalty, the first of three in the match to open the scoring.
But Man United wasted no time responding as Bruno Fernandes equalised with a penalty after Rasmus Hojlund was brought down.
He then added a second shortly after halftime, following a lengthy VAR review for a foul on Patrick Dorgu.
Real Sociedad's aspirations took another hit when Jon Aramburu received a straight red card for a reckless foul on Dorgu during a counter-attack.
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Fernandes capped off his treble with a precise low finish, bringing his total Europa League tally to an astonishing 24 goals and 17 assists.
Despite this resounding victory, one Man United fan named Mike, calling into talkSPORT, expressed profound dissatisfaction to hosts Jamie O'Hara and Jermaine Pennant.
"I'm not happy if we win it (the Europa League) because they're just going to do exactly what happened under Erik ten Hag: it's the players' fault, it's okay, we can just paint over it. We've got to clear the dead wood out," he insisted.
Former Tottenham star O'Hara and ex-Liverpool man Pennant were astounded.
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"Are you telling me you don't want Man United to win the Europa League? Is there something wrong with you?" O'Hara exclaimed.
Mike countered, "Yeah, we're 14th in the Premier League, which is disgusting by the team's standards. I'd just leave this, let it go."
"What are you talking about!? If you win the Europa League, you get the Champions League; it's worth millions of pounds.
"If you don't win the Europa League, you're not in Europe. Who are you going to sign? Who is going to sign for Man United if you finish 14th in the Premier League table, don't win a trophy, and haven't got European football next season? What are you talking about, Mike? You're talking garbage," O'Hara retorted.
The debate heated up, with Mike contending that a Europa League victory would merely mask deeper issues within the squad.
O'Hara, along with Pennant, stressed the undeniable benefits of winning the trophy: Champions League qualification and substantial financial rewards.
"Mike, mate, I don't know if you're being real," O'Hara said in disbelief.
"I can't understand what you're saying. I understand you want to get rid of the dead wood, but the club still has a chance to win a trophy, a major honour, and get Champions League football, which is worth millions to the football club.
"You'll have eight games guaranteed in the Champions League if you win the Europa League. Revenue for Sir Jim Ratcliffe."
The conversation spiralled into a cycle of frustration, with O'Hara and Pennant grappling to understand Mike's viewpoint.
"It's like banging my head against a wall," O'Hara lamented.
Manchester United will now quarter-finals against Lyon, who triumphed over FC Steaua Bucuresti.
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Should they beat the French side then a tie with Athletic Bilbao or Rangers will await them in the semi-final.
And an all-English Tottenham with Tottenham remains on the cards after the overturned a 1-0 first leg deficit to claim a 3-2 aggregate triumph.
talkSPORT goal panel react as Manchester United beat Real Sociedad to progress in the Europa League
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