Leading 1-0 from the first leg, United took control as Marouane Fellaini's headed home Marcus Rashford's cross.
But Celta, needing two goals, levelled on the night through Facundo Roncaglia to set up a nervy finish.
United's Eric Bailly and Roncaglia were sent off after a mass brawl as the hosts joined Ajax in the final.
The Red Devils will meet the Dutch side, who beat Lyon in the other semi-final, in Stockholm on 24 May, with the winners guaranteed a place in next season's Champions League.
Manchester United a step closer to first Europa League triumph
Reviewed by Debo Olowu
on
May 11, 2017
Rating:
Reviewed by Debo Olowu
on
May 11, 2017
Rating:
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