The away goal means United will bve heavy favourites to progress to the final of the competition when the sides play the second-leg of this tie, next week.
United were the better team throughout, although they missed a number of gilt-edged opportunities.
In the first half, both Henrikh Mkhitaryan and Jesse Lingard missed point-blank chances to leave Jose Mourinho fuming on the touchline.
In the second half Lingard missed another fine chance from close-range before Rashford hit his winner.
Celta had chances of their own and Iago Aspas went close with a header, but ultimately did not have enough to truly test their more cultured opponents.
How did we rate the players in United's crucial away win? Take a look at the gallery above to find out.
Do you agree with our ratings? Who was your man of the match? Let us know in the comments...Reuse content