Goals by Jack Collison, Junior Stanislas and Guillermo Franco plus penalties by Carlton Cole and Luis Jimenez put Gianfranco Zola's East Enders into a five-goal lead before Steven Fletcher's double and Chris Eagles' stoppage-time strike added some respectability to the scoreline for the visitors, who also had skipper Steve Caldwell dismissed for a professional foul, late on.
After seeing his sloppy side toss away a two-goal lead at Hull City last Saturday, the Italian had made three changes to his 17th-placed side that had finally drawn 3-3 with the tenacious Tigers, as Jonathan Spector, Radoslav Kovac and the fit-again Herita Ilunga replaced Valon Behrami, Matthew Upson (hamstring) and substitute Julien Faubert.
Franco had opened the scoring at the KC Stadium and, seven days on, the Hammers striker almost repeated the feat, when he met Collison's 12th-minute cross with a brave header that saw the ball crash off the bar and the Mexican receive treatment following a clash of skulls.
That rare raid had been the only threat to the hitherto redundant Brian Jensen but, on 18 minutes, West Ham broke the deadlock against the run of play, when Scott Parker's quick free-kick released Collison behind the static Burnley defence and, with just the helplessly exposed Clarets keeper to beat, the Wales international calmly slotted home his second goal of the season.
Then on 33 minutes, the Hammers doubled their lead when Cole's presence and power allowed him to pick out Franco, whose exquisite reverse pass left Stanislas facing Jensen and, although his angled shot was blocked by the keeper, the England Under-21 winger reacted first to send his second bite of the cherry in-off the far post.
And two minutes before the break, West Ham gave themselves a three-goal interval cushion, when Cole - who had earlier been wiped out by the on-rushing Jensen - sent an ice-cool spot-kick back past the Dane, after Robbie Blake had tripped the steam-rollering Spector.
Just how 11th-placed Burnley had trudged off at the break three goals adrift was a mystery to the long-suffering, travelling supporters amongst the 34,003 crowd.
Indeed, Owen Coyle had named an unchanged team following last week's draw against Aston Villa and, in the early stages, the visitors had hardly looked like a side that has only garnered one point on their travels as Andre Bikey saw his close-range volley cannon off Robert Green's torso and Parker block climbing Clarke Carlisle's header on the line, after the Clarets defender rose highest to meet Blake's corner.
That opening quarter-hour was a dim and distant memory for bedraggled Burnley as they emerged for the restart, though and, on 51 minutes, Franco claimed his third goal in English football, when he got in front of Bikey to nod home Stanislas' free-kick.
After failing to shake off the effects of that earlier juddering Jensen challenge, Cole had been replaced by Zavon Hines at the break and, as the hour-mark approached, Jimenez then replaced Franco, who departed to rapturous applause.
Within three minutes of his arrival, the Chile international found himself on the scoresheet, too, when he dusted himself down and lashed home the consequent penalty after being tripped by Jensen as he attempted to circumnavigate the diving Dane.
But despite being five goals adrift, Burnley commendably refused to raise the white flag and, midway through the second period, Fletcher popped up at the far post to tap home Eagles' low cross.
And with a quarter-hour remaining, the pair combined once more to carve out a carbon-copy second that saw Fletcher prod home his eighth goal of the campaign.
Not even Caldwell's late dismissal for pulling back the escaping Hines could dampen their enthusiasm and Eagles turned in ex-Hammer Tyrone Mears' cross for Burnley's third but, despite having surrendered the lead five times this season, not even West Ham could contrive to throw away their diminishing two-goal cushion in the dying moments.