West Ham's front three each played a role in one of the goals as Manuel Pellegrini's side stretched their unbeaten run to four with their biggest win over United in 36 years.
That helped the Hammers get off to a flying start as summer signing Felipe Anderson opened his account for the club by finishing off a well-worked move on six minutes.
United failed to register a shot on target during the first half but did hit the post when Romelu Lukaku met Ashley Young's near-post delivery with a header which came back off the outside of the woodwork.
Despite the public development of his feud with Mourinho this week, Paul Pogba was included in United's starting lineup but he could not inspire a response from the visitors who were short of creative ideas.
Things went from bad to worse for the Red Devils before half time as their failure to clear a corner allowed Andriy Yarmolenko to work a shot on his left foot, although only a huge deflection from Victor Lindelof took it past De Gea, who was on his way to the opposite corner.
West Ham had a couple of opportunities to extend their lead early in the second period, with Marko Arnautovic blazing a volley high and wide at the end of a slick counter, and then being the victim of a poor pass from Anderson who should have teed up the Austrian for a one-on-one.
One of Mourinho's methods to get back into the game was to throw Marouane Fellaini forward, and the Belgian nearly reduced United's deficit with a powerful 65th-minute header which Lukasz Fabianski did well to claw off the line.
Another was to bring on Marcus Rashford, who, returning from a three-match suspension, pulled one back for United on 71 minutes when he connected sweetly with a near-post flick from a corner, catching Fabianski by surprise.
United's comeback was nipped in the bud within three minutes when Noble's through-ball pierced the heart of the visiting defence and found the run of Arnautovic, who buried his shot past De Gea for his fourth goal of the campaign.
The 13-time Premier League winners now have their worst points return after seven games of a season, and Mourinho invited extra scrutiny upon himself by hooking Pogba with 20 minutes to go.
WEST HAM (4-3-3): Fabianski; Zabaleta, Balbuena, Diop, Masuaku; Rice, Obiang, Noble; Yarmolenko (Snodgrass, 72'), Anderson (Diangana, 90'), Arnautovic (Antonio, 83')
MAN UTD (3-5-2): De Gea; Young, McTominay, Smalling, Lindelof (Rashford, 57'), Shaw; Fellaini, Matic, Pogba (Fred, 70'); Martial (Mata, 71'), Lukaku