BURNLEY made it a hat-trick of wins for the first time this season to end a 38-year wait for a win at Upton Park.
And like last week at Hull, they came back from behind to secure the points, with Sam Vokes the matchwinnner.
After a goalless first half in which West Ham applied plenty of pressure, the home side took the lead seven minutes after the break.
Kevin Nolan had posed a big threat with his midfield bursts into the box and his eyes lit up when Robert Green's long kick was flicked into his path.
With Lee Grant caught off his line, the former Bolton and Newcastle midfielder lobbed the keeper.
But Burnley were level within the space of five minutes thanks to captain Chris McCann's third goal in two games.
Junior Stanislas, playing against his old club for the first time since leaving in August, whipped an inviting ball into the box from the right, and McCann headed powerfully past Green.
Targetman Vokes, who like McCann was also on the scoresheet against Ipswich, came off the bench to head in a 75th minute winner – thumping in fellow substitute Ross Wallace's outswinging corner, after Green tipped Jay Rodriguez's 40-yard shot around the post.
West Ham piled the pressure on again, but Burnley defended for their lives.
Their determination and resilience paid off as the Clarets have now climbed to 10th in the Championship, five points adrift of the play-off places.