A goal in each half from David Nugent and Danny Fox condemned West Ham United to a first Barclays Premier League defeat of 2010 despite a late consolation from debutant Ilan.
Gianfranco Zola's men were caught out by Nugent's opportunist effort early in the first half. Fox then doubled the agony with his free-kick just before the hour and it seemed an impossible mission despite the best efforts of the Hammers in the second half. Ilan did give some late hope with a goal on his debut but the home side held on in the face of fierce pressure.
The visitors had Carlton Cole - making his first start since the 28 November meeting between the clubs - back in attack alongside new recruit McCarthy. Radoslav Kovac had made way for McCarthy, who lasted 45 minutes before being replaced by Mido, another new arrival.
The first quarter of an hour was a scrappy affair with the Hammers continuing where they had left off from last Saturday's goalless draw at home to Blackburn Rovers. Burnley had the better of the opening period, forcing a couple of corners before breaking the deadlock on 14 minutes.
Left-back Fox, making his debut after his switch from Celtic, pumped the ball forward for Nugent to chase. The striker, who has just extended his loan from Portsmouth until the end of the season, burst into the penalty area ahead of Matthew Upson before lobbing the ball over the on-rushing Robert Green and into the empty net.
West Ham improved after going a goal behind and had three good opportunities in quick succession midway through the half. McCarthy twice, Jack Collison and Cole all got into good positions but could not convert. Scott Parker, in for the injured Alessandro Diamanti, then surged forward on 33 minutes before sliding the ball through to McCarthy.
He rounded Brian Jensen but his shot was hacked away by Cort. It was to be his last notable contribution as he got a knock that forced him off at half-time - leading to Mido's arrival as a West Ham United player. The Eygpt forward fired his first effort goalwards on 48 minutes, only for it to fizz just wide of Jensen's right-hand post.
The Hammers seemed top but Jack Collison put the Hammers on the back-foot when he pushed over Tyrone Mears just outside the penalty area ten minutes into the second half. That allowed Fox the chance to step up and curl an exquisite free-kick into the top corner. Parker so nearly pulled one back immediately but Jensen dived low to his left to palm his shot round for a corner.
Cole thought he had equalised on 66 minutes when he scrambled in a goalbound shot by James Tomkins from a Julien Faubert cross. The England man had come from an offside position though and referee Howard Webb - a late change for Steve Bennett - brought a swift end to any Hammers celebrations.
Stanislas crashed a free-kick against the crossbar on 72 minutes but Burnley remained a threat the other end with Steven Fletcher and Nugent keeping Upson and Tomkins on their toes.
Ilan made it a goalscoring start to his Hammers career when he lashed in from ten yards after Mido's effort had been blocked. He then went close with another effort before Mido crashed Cole's low cross against the post.
While Burnley remained a threat on the break, it was the visitors who threw everything forward in search of an equaliser, only for Jonathan Spector, Parker and Cole to hit efforts off-target when well placed.
Click here for the team-sheet