Michail Antonio scored the only goal of the game in the ninth minute to wrap the three points up for the Hammers.
Pablo Fornals supplied the cross from the left hand side and the 30-year-old forward stole a yard from Robbie Brady to touch the ball home from close range.
The Clarets cranked up the pressure in the second half - with Dwight McNeil, Matej Vydra and Jay Rodriguez featuring from the bench - but they couldn't force an equaliser.
Here are the ratings...
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Sean Dyche, Manager of Burnley reacts during the Premier League match between West Ham United and Burnley FC at London Stadium on July 08, 2020 in London, England. Photo: Adam Davy
. Nick Pope 6
Yet again, didn't have a great deal to do. Left completely exposed by his defence for West Ham's winner, but wasn't tested for the remainder. Vocal and commanded his penalty area well. Photo: Catherine Ivill
. Matt Lowton 6
Got forward well in support of Burnley's attacks and produced a number of pinpoint crosses that were begging to be put away. Question marks over whether he could have done more to close Fornals in the lead up to West Ham's winner. Photo: Gareth Fuller
. Erik Pieters 4
Did well to initially snuff out the danger in the lead up to Antonio's winner, forcing Bowen wide. Caught out of position a number of times and much of West Ham's success - when breaking into the box - came down his side of the pitch. Photo: Rui Vieira
. James Tarkowski 6
Poor communication led to West Ham's opener as Mee took the ball off his head from a Fornals cross. Got in the way of plenty inside his own box to prevent the Hammers extending their lead and posed a physical threat at the other end of the pitch. Photo: Gareth Fuller
1. Nick Pope 6
Yet again, didn't have a great deal to do. Left completely exposed by his defence for West Ham's winner, but wasn't tested for the remainder. Vocal and commanded his penalty area well. Photo: Catherine Ivill
2. Matt Lowton 6
Got forward well in support of Burnley's attacks and produced a number of pinpoint crosses that were begging to be put away. Question marks over whether he could have done more to close Fornals in the lead up to West Ham's winner. Photo: Gareth Fuller
3. Erik Pieters 4
Did well to initially snuff out the danger in the lead up to Antonio's winner, forcing Bowen wide. Caught out of position a number of times and much of West Ham's success - when breaking into the box - came down his side of the pitch. Photo: Rui Vieira
4. James Tarkowski 6
Poor communication led to West Ham's opener as Mee took the ball off his head from a Fornals cross. Got in the way of plenty inside his own box to prevent the Hammers extending their lead and posed a physical threat at the other end of the pitch. Photo: Gareth Fuller