In a game of sporadic chances at both ends it was fans favourite Michail Antonio’s early strike that made the key difference.
The Hammers looked positive in the opening minutes in East London and Antonio seized his opportunity to put them ahead on nine minutes.
Pablo Fornals’ whipped cross deceived Clarets defender James Tarkowski and Antonio kept his cool to fire past Nick Pope.
Moyes’ hosts could and should have extended their lead just before the break but Angelo Ogbonna’s header clattered back off the post.
West Ham continued to edge things after the restart with Jarrod Bowen flashing an effort just wide and Declan Rice testing Pope.
But despite dominating the majority of the game, West Ham’s inability to find a second goal almost came back to bite them as Dwight McNeil and Jay Rodriguez both wasted half chances but the Hammers had just enough to hold on.
Full Time from the London Stadium it’s West Ham 1 Burnley 0