The fervent home fans were enraged when Athletic defender Daniel Vivian was sent off for pulling back Rasmus Hojlund and Fernandes slotted home the resulting penalty, after Casemiro had opened the scoring against the run of play in the semi-final first leg.
Fernandes rolled in a third before half-time as Ruben Amorim's side moved a step closer to the final, to be held at Athletic's San Mames stadium.
The hosts have been dreaming of winning a first European trophy on their own soil, but their hopes were demolished by United's professional display in the north of Spain - and Athletic's supporters argued about the refereeing.
Languishing in 14th in the Premier League, Champions League qualification for United is only possible with a Europa League triumph, as is access to the £100 million honeypot it entails.
Despite regularly crumbling under pressure this season, the Red Devils - who produced a stunning comeback against Lyon in the quarter-finals - first survived and then thrived in a hostile environment.
Man Utd boss Ruben Amorim warned his side they "need to be prepared" when they face Athletic Bilbao in the return leg at Old Trafford next week.
"The result is really good, but we have to understand the result at the same time," he said to TNT Sports.
"We struggled a lot at the beginning and the sending off changed the game. Any game can change with one situation. We had an opportunity to score one more. This is not done and they can do the same at Old Trafford.
"They're really strong and intense. We need to be prepared. Manuel Ugarte with a lot of experience was a little nervous, Patrick (Dorgu) was nervous. Players like Casemiro, Harry Maguire, Bruno Fernandes help a lot.
"Of course we have an advantage. We have our fans, but again this could change. Anything can happen in one game.
"We need to be really careful with our players against Brentford (on Sunday). Noussair Mazraoui is dead, Patrick Dorgu is tried - we have to manage the players."
With May 1st a bank holiday in Spain the streets of Bilbao were filled with red-and-white striped shirts from the morning onwards, in party mode.
The San Mames was rocking as fans greeted their heroes, all of them born or raised in the Basque country, as per the club's century-long policy.
Alejandro Garnacho's early strike gave the hosts a scare but the forward was offside.
Beyond that the early stages of the match for United were about gritting their teeth and holding off the Basque side and their raucous supporters.
Red card rocks hosts
Alex Berenguer forced a smart low save from Manchester United goalkeeper Andre Onana, and Inaki Williams headed narrowly over.
Victor Lindelof made a vital block to thwart Berenguer after Nico Williams fed his brother Inaki, who was given too much space on the right wing.
The hosts were ascendant and when former Real Madrid midfielder Casemiro opened the scoring for United it came as a shock.
Just as much of a surprise was the way United created the goal, with centre-back Maguire dribbling down the right flank as Mikel Jaureguizar floundered in his wake.
The defender fizzed a cross into the area, which Manuel Ugarte flicked on to the back post for Casemiro to nod home from close range.
It seemed like a smash-and-grab but soon United had a second, when Vivian was penalised for pulling back Hojlund as he tried to connect with a cross.
The defender was sent off to add insult to injury, as Athletic fans howled in anger, and Fernandes rolled home from the spot.
Athletic coach Ernesto Valverde made a double substitution, trying to stem the bleeding, but his team shipped a third before half-time.
Ugarte's clever backheel played Fernandes through on goal and he stroked home with ease.
Noussair Mazraoui crashed a shot off the crossbar from distance as United almost grabbed a fourth before the break.
Norwegian referee Espen Eskas and his colleagues were barracked by the home fans, seeing their aspirations to glory evaporate before their eyes.
They were further enraged, waving anything white to show their disgust, when Maroan Sannadi tumbled under pressure from Maguire as he ran towards goal but no foul was awarded.
United largely controlled the game in the second half but they could not add a fourth despite probing.
"We looked a little bit nervous at times in the first 20 minutes... we weathered the storm and we knew we'd get our chance," United's Harry Maguire told TNT Sports.
"It was a clinical first half, professional second half... It's a great victory in the end but there's another big game next week."
The second leg takes place next Thursday at Old Trafford, ahead of the final on May 21 against Tottenham or Bodo/Glimt.
"At the slightest contact (Hojlund) let himself fall and the bad luck is that the penalty was given," said Inaki Williams.
"We weren't particularly great, so we shouldn't make excuses - we're three goals down but we're capable of mounting a comeback."