Real Sociedad took the lead through Mikel Oyarzabal with the first of three penalties of the last 16 second leg clash.
United fought back moments later when Fernandes was tasked with scoring from 12 yards after a foul on Rasmus Hojlund.
The captain successfully drew his side level and set a Europa League record in the process.
Fernandes scored his ninth ever penalty in Europe's second-tier competition, the most in its history.
He extended his spot-kick tally to ten during the opening moments of the second half after a long VAR check for a foul on Patrick Dorgu.
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Real Sociedad's hopes of levelling on the night and on aggregate over the tie were all but ended when they went down to ten men.
Jon Aramburu was shown a straight red card when he brought down Dorgu as the last man against a United counter-attack.
Ruben Amorim's side thought they won a third penalty late on but Dorgu was adjudged to have not been fouled after a swift VAR check.
Cameras later caught Dorgu telling the referee that Hamari Traore legally won the ball off him when making the tackle.
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However, Fernandes was on hand to complete his hat-trick moments later, this time with a low finish into the bottom corner.
His tally has now reached 15 in all competitions for the season, with four of those now coming in the Europa League.
Diogo Dalot scored the fourth and final goal in the Old Trafford rout with a close range finish in stoppage-time.
However, it's Fernandes who takes the headlines with a real captain's performance as United kept their hopes of winning silverware alive.
They will now play in the quarter-finals against Lyon, who beat FC Steaua Bucuresti 7-1 on aggregate in their last 16 clash.
Victory is their first after a winless run of three in all competitions and sees them remain unbeaten in the Europa League.
United are one of the stronger sides on their side of the draw alongside Athletic Bilbao and one of Rangers and Fenerbahce.