Ole Gunnar Solskjaer's side needed an extra-time winner from in-form midfielder Scott McTominay to claim a 1-0 win over the Hammers at Old Trafford and secure their place in the quarter-finals of the FA Cup.
In doing so, United extended their home winning run in the competition to nine consecutive matches which saw the club equal it's longest such sequence in the competition since 1912, according to Opta.
The occasion also saw forwards Marcus Rashford and Anthony Martial reach notable milestones for the club, with the duo both making their 250th appearance for the Red Devils.
In the evening's other match, Championship side AFC Bournemouth knocked out Premier League outfit Burnley after recording an impressive 2-0 win away from home.
Glenn Murray has joined Nottingham Forest from Brighton & Hove Albion
Denmark international Jonas Lossl has returned to boyhood club FC Midtjylland after leaving Everton
Greek giants Olympiakos have signed Kenny Lala from Strasbourg
Union Berlin have signed Croatian striker Petar Musa on a season-long loan from Slavia Prague
Brentford have signed Winston Reid on loan from West Ham United
Ukraine star Victor Kovalenko has signed for Atalanta from Shakhtar Donetsk
Jeremain Lens has joined Fatih Karagumruk on loan from Besiktas
Bayern Munich have loaned USA starlet Chris Richards to Hoffenheim.
Brighton & Hove Albion have signed Ecuador wonderkid Moises Caicedo from Independiente del Valle
AS Roma have signed Bryan Reynolds from FC Dallas.
Nemanja Radonjic has joined Hertha BSC on loan from Olympique Marseille
Hertha BSC have signed Sami Khedira from Juventus
Joshua Zirkzee has joined Parma on loan from Bayern Munich, with the Serie A side retaining the option to make the move permanent at the end of the season
Galatasaray have signed for DeAndre Yedlin and Gedson Fernandes
Liverpool have signed defender Ben Davies from Preston North End
Southampton signed Japan international Takumi Minamino on loan from Liverpool
Morocco star Oussama Idrissi has joined Ajax Amsterdam on an initial loan deal from Sevilla
Daniele Rugani completed a loan move to Cagliari from Juventus
Everton have signed Joshua King from Premier League from Championship side AFC Bournemouth
Jean-Clair Todibo has joined OGC Nice on loan from Barcelona