The Hammers, with only one win in the previous 19 top-flight meetings, were ahead after just five minutes through club-record signing Felipe Anderson's clever back-heeled finish from Pablo Zabaleta's cross - despite both players appearing to be offside.
And the hosts doubled their advantage on the brink of half-time in fortunate fashion, as Andriy Yarmolenko's shot cannoned in off Victor Lindelof and beyond the wrong-footed David de Gea.
Marcus Rashford responded for the largely pedestrian visitors on 71 minutes, but Marko Arnautovic restored the Hammers' two-goal lead less than three minutes later as Mark Noble's pass sliced through United's unconvincing back-line.
The Red Devils also picked up 10 points from their opening seven fixtures in 2013-14 under David Moyes, but their margin of defeat made this their worst top-flight start since they accrued just seven points in 1989-90.
Manchester United proved no match for a lively West Ham in the opening stages, but the visitors did go close to equalising when Romelu Lukaku's header struck the post midway through the first half.
Their appeared little response to their midweek Carabao Cup exit to Championship side Derby, however, and the Hammers - who had failed to score in their previous three home games - enjoyed plenty of chances.
Marouane Fellaini forced a magnificent save from goalkeeper Lukasz Fabianski as the visitors chased a route back into the contest, before Rashford's sublime front-post flick offered a lifeline.
But Arnautovic's fourth goal of the season signalled West Ham are beginning to progress under Manuel Pellegrini, while problems continue to mount for Manchester United and manager Mourinho.
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Premier legue