In their first ever European semi final, the hosts did not look to be any better than their 11th position in La Liga suggests, on the back of three straights domestic defeats.
United know that - had it not been for the brilliance of goalkeeper Alvarez - the tie would be all but won ahead of next Thursday's Old Trafford return.
It's far from over at 1-0, but United should have every confidence of progressing to a first European final for six years.
Marcus Rashford capped his man of the match showing with a superb goal, Jesse Lingard was impressive and Henrikh Mkhitaryan again lively.
Paul Pogba showed United what we've been missing during his injury enforced absence with a dominant midfield performance.
The Reds have looked slow and sluggish without the Frenchman's power in midfield recently and he ran Rashford close as our most impressive player against Celta.
He linked up well with United's front three and pushed the Spanish side on to the back foot with his pace and surging runs as he dictated the game in a more advanced role.
Eric Bailly remarkably recovered from the knee injury he sustained against Swansea to make an immediate return to the heart of the defence.
Chris Smalling also returned as a late substitute but Ashley Young - himself a replacement for Mkhitaryan - limped off with a hamstring problem only eleven minutes after he had come on.
Rashford also limped off late on but played with a minor problem and was taken off as a precaution.
United's long and gruelling season - this was our 58th match of the campaign - has taken its toll and stretched the squads to the limit, both physically and mentally.
United face a testing domestic run-in, with trips to Arsenal and Spurs followed by Southampton away and Palace at home.
In a bid to keep the first team players fresh and injury free for the final, Jose looks set to shuffle his pack and involve several of the squad's young fringe players for the four remaining league games.
United's road to Europa League glory is nowhere near as bumpy as that to a top four finish, with a coveted return to the Champions League potentially one win away.
United's European journey started out in Rotterdam against Feyenoord and now looks set to come full circle in Stockholm.
Fellow Eredivisie side Ajax stormed to a 4-1 first leg win over Lyon in their semi and, barring a magnificent comeback from the French team, will provide the final hurdle of a season that still has plenty to offer.