United Hammer On
Cristiano Ronaldo wasn't in sparkling form, with United forced instead to rely on the old guard of Ryan Giggs and Paul Scholes to win them their three points.
In-form striker Cole, who was called into the England squad on Saturday, was played through by Jack Collison and, after shrugging off Rio Ferdinand, tried an audacious chip which was easily saved. Rising star Collison then wriggled his way into the United box but his lay-off to Cole was just behind the striker and allowed the visitors to clear.
United were also passing the ball around with their customary ease and authority, although without penetration, and found West Ham's defence in just as stubborn mood as their own.
Former Hammers player Carlos Tevez was being well-marshalled as the both midfields wrestled for superiority.
United did come close to a breakthrough when an off-target Paul Scholes strike was diverted goalwards by Cristiano Ronaldo, who saw keeper Robert Green tip the ball over.
But Sir Alex Ferguson's side pose a threat from every department and it was the veteran skipper Giggs who rolled back the years to put his side ahead after collecting a sweeping Scholes pass. He cut inside the diving challenge of Cole and into the Hammers box from the left before curling a low right-footed shot through a crowd of players for his first league goal of the season.
Ronaldo could have had a penalty late on after a trip by Neill but referee Phil Dowd waved away his appeals. Ultimately, the visitors comfortably secured a 1-0 victory - their ninth by that scoreline in the league this season - that lifts them two points clear of rivals Liverpool.
West Ham: Green, Neill, Collins, Upson, Ilunga, Behrami (Tristan 87), Parker, Noble (Nsereko 77), Collison, Cole, Di Michele.
Subs Not Used: Lastuvka, Boa Morte, Kovac, Spector, Sears.
Man Utd: Van der Sar, Rafael Da Silva, Ferdinand, Vidic, O'Shea, Ronaldo, Scholes, Carrick, Giggs, Tevez (Park 87), Berbatov.
Subs Not Used: Foster, Nani, Welbeck, Fabio Da Silva, Fletcher, Eckersley.
Goals: Giggs 62.
Ref: Phil Dowd (Staffordshire).