Brighton created some promising opportunities with just the one goal in it, but they could not find a way through as their hopes of reaching just a second semi-final came to an end.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Romero; Valencia, Bailly, Smalling, Shaw; Matic, McTominay; Mata, Lingard, Martial; Lukaku
SUBS: De Gea, Lindelof, Young, Fellaini, Pogba, Sanchez, Rashford
STARTING XI: Krul; Schelotto, Duffy, Dunk, Suttner; Gross, Propper, Kayal, March, Locadia; Ulloa
SUBS: Maenpaa, Bruno, Goldson, Sanders, Izquierdo, Baldock, Murray
Jose Mourinho: "Every match is important. We train very well, always. We train always very, very well, so we don't need a reaction to train better than we do because the training, the professionalism, the enthusiasm, the organisation, every training session with us since day one, since I arrived, the players have been absolutely brilliant."
Chris Hughton: "What we all know about United is they have huge quality, and are only second in this division because Manchester City are having an outstanding season. They are going to have days that are not so good, and we'll have to make sure that we play well enough to get a result. To go through would be wonderful for this club."
MANCHESTER UNITED SUBS: De Gea, Lindelof, Young, Fellaini, Pogba, Sanchez, Rashford
BRIGHTON & HOVE ALBION SUBS: Maenpaa, Bruno, Goldson, Sanders, Izquierdo, Baldock, Murray