Jack Collison opened the scoring after 17 minutes when he latched onto a Scott Parker free-kick inside the box and tucked his shot into the bottom corner of the goal.
West Ham never looked back from this point and 15 minutes later Junior Stanislas doubled the scoreline. The Burnley defence failed to close him down and Stanislas' low shot beat Brian Jensen from 12-yards out.
The game was arguably dead and buried before half-time as Carlton Cole netted the third from the penalty spot. Jonathan Spector was brought down inside the box by Robbie Blake and England International Cole sent Jensen the wrong way.
Guillermo Franco got his name on the score sheet moments after the interval as he nodded home a Stanislas free-kick before Gianfranco Zola's side were awarded another penalty - this time converted by substitute Luis Jimenez, who had won the spot-kick.
It looked set to be an embarrassing afternoon for Owen Coyle's men, however they never gave up and got their reward on the 67th minute when Steven Fletcher steered a Chris Eagles cross past a helpless Robert Green.
The goal sparked a mini revival from the visitors and Eagles gave Jonathan Spector a torrid time on the left flank, setting up Fletcher's second with almost an action replay of the previous goal.
The misery was completed for Burnley in injury time as Steven Caldwell was dismissed for a professional foul on Zavon Hines, but winger Eagles pulled another back for the Clarets in the dying moments to make the defeat a little more respectable.