Man United smother Celta 1-0
The visitors were denied on three separate occasions in the first half before Marcus Rashford scored on a direct free kick in the final quarter of regulation.
The outcome means that the Red Devils need only a scoreless draw in the second leg at Old Trafford to advance to the final.
Celta enjoyed an extended spell of possession in the early going and appeared set to take a 1-0 lead in the 11th minute when Nemanja Radoja's cross found Daniel Wass in scoring position inside the six-yard box, but the Danish international's header missed the target.
The hosts lacked their characteristic flair and boldness on the attack.
United, without injured top scorer Zlatan Ibrahimovic, were content to wait for a chance on the counter and rely on the individual quality of players such as Paul Pogba.
It was only the heroics of goalkeeper Sergio Alvarez that kept Celta from ending the first half down 3-0.
He made a spectacular stop against Rashford in the 20th minute and thwarted Henrikh Mkhitaryan 15 minutes later. With six minutes left before the half-time whistle, Alvarez shined again with a great save against Jesse Lingard.
Celta showed signs of life after the re-start.
Iago Aspas threatened with a header in the 51st minute and United keeper Sergio Romero had to be sharp to deal with Pione Sisto's dangerous strike in the 58th.
Yet the home side remained disjointed on offense, as the trio of Sisto, Aspas, and John Guidetti failed to link up.
Rashford's goal in the 67th minute sucked all of the air out of Vigo's Balaidos stadium and Celta menaced the United goal only once more before the final whistle.