The Hammers started the brighter of the two sides and were unlucky not to take a lead into the break after securing much of the possession and territory.
Captain Kevin Nolan then found himself on the end of a long clearance by Rob Green to volley and unstoppable shot past Lee Grant in the Burnley goal.
Burnley then hit back against the run of play, almost immediately, after a good cross by former Hammers Junior Stanislas found Chris McCann to equalise.
West Ham’s domination continued but they were unable to find the killer goal. They were then undone by a Sam Vokes header on 85 minutes to inflict another home defeat on Big Sam’s side.