Felipe Anderson scored a second-half brace as West Ham held on and stave off a late fightback from Burnley who came from behind twice to try to snatch a point at the London Stadium.
Marko Arnautovic broke the deadlock after 10 minutes following a mistake by Tarkowski just before the West Ham striker scored. Johann Gudmundsson then sprung the offside trap to finish neatly and level things up on the stroke of half time.
Felipe Anderson restored the Hammers lead in the second half as he broke through and finished well on his left foot following a good bit of play from Arnautovic and Diangana.