Dawson headed into his own net in the second half as United moved back up into second place and the Hammers missed the chance to put the pressure on their Champions League rivals.
The result means United climb above Leicester and now have a nine-point cushion to West Ham in fifth place.
Here is how Jack Rosser rated the sides at Old Trafford…
Manchester Utd (4-2-3-1): Henderson 6, Wan Bissaka 6, Lindelof 6, Maguire 8, Shaw 7, McTominay 6, Fred 6, Greenwood 7, Bruno Fernandes 5, James 5, Rashford 6.
Subs not used: Bailly, Grant, Diallo, Alex Telles, Bishop, Matic, Williams, Tuanzebe, Shoretire.
West Ham (5-3-2): Fabianski 6, Coufal 7, Dawson 5, Diop 6, Cresswell 6, Soucek 5, Rice 6, Johnson 5 (Benrahma 6), Noble 5 (Lanzini 6), Bowen 5, Antonio 5.
Subs not used: Balbuena, Alves, Martin, Trott, Odubeko, Coventry.