Due to travel restrictions in Spain, this tie took place in Turin, meaning La Real lost the advantage of playing in their home stadium.
Billed as one of the ties of the round, it lived up to expectations with both attacks looking dangerous in the first half and Marcus Rashford should have opened the scoring early on when put through, but shot straight at goalkeeper Alex Remiro.
United did open the scoring on 27 minutes as Remiro clattered into defender Robin Le Normand, allowing Fernandes to tap into an empty net from close range and net his 20th goal of the campaign in all competitions.
La Real finished the half the stronger but, despite some shaky United defending, the "home" side failed to take advantage.
Former United academy graduate Adnan Januzaj was up against his old side for the first time since his departure for Spain in 2017 and told ESPN on the eve of the match that he had nothing to prove.
Fernandes made it 2-0 on 57 minutes after cleverly stepping over a Rashford through ball, which found Daniel James who slipped in the Portugal midfielder. The goal was initially ruled out for offside, but a VAR review overruled the original decision and referee Sandro Scharer awarded the goal.
United's third came 64 minutes as Rashford ran on to Fred's pass to poke the ball past Remiro and put Ole Gunnar Solskjaer's side in firm control of the tie.
The Wales international did eventually make it 4-0 with a close-range finish in the 89th minute.
United, who won the trophy in 2017, are among the favourites and Fernandes said they plan on going all the way after being knocked out of the Champions League at the group stage.
"We're in this competition to win it," he said.
"My target is scoring the most goals I can and trying to assist my teammates in scoring too. My target is trophies, and winning trophies is more important than scoring goals.
"Today I think we did everything well. We still have the second leg and a tough game at home; 4-0 is a good result but we have to be aware of what Real Sociedad can do."
Solskjaer praised Fernandes for his effort.
"He's good at finding spaces and his technical ability when it comes to chances is top class. Two very good goals," Solskjaer said. "Bruno always wants to do the next thing correctly. He wants to do the next thing at the best of his ability and that is a very good attribute and quality to have. You never rest on your laurels."
He added that least season's semifinal run in the competition, in which United lost to eventual champions Sevilla FC, has helped inspire this season's campaign.
"I think the experience from last season has helped this team, these boys, and we have got to learn from experiences on the job," Solksjaer said. "That's the only way of learning from your mistakes to correct them."
The second leg will be played next Thursday at Old Trafford.