Goals from Charlie McNeill and Alejandro Garnacho set up a final at the Theatre of Dreams against either Nottingham Forest or Chelsea.
The Under-18s have triumphed over Scunthorpe United, Reading, Everton, and Leicester City to secure their place in the one-legged fixture.
United are the most successful club in FA Youth Cup history, with 10 tournament victories, and the side that last lifted the trophy 11 years ago included current first-team players Paul Pogba and Jesse Lingard.
United dominated the first half, with a strong Garnacho run in the box earning the first in a succession of corners.