On another afternoon of high drama at the London Stadium the Clarets conceded two late goals to suffer a third successive Premier League defeat.
Last season’s 3-0 win here for the Clarets was marred by a series of pitch invasions by unhappy Hammers fans.
But this time they were celebrating at the end after goals from Felipe Anderson and Javier Hernandez ended a four-match winless run.
The Clarets twice hit back to level through Johann Berg Gudmundsson and Chris Wood.
And when Wood - whose two goals from the bench in last season's win had helped sparked the unrest - headed his first league goal of the season with 13 minutes to go it looked as though Sean Dyche’s men might escape with a point.
But Anderson’s second goal of the game and Hernandez’s injury-time effort put paid to those hopes as the Clarets’ defensive problems again proved costly.
Dyche’s response to back-to-back defeats to Manchester City and Chelsea was to make three changes to the Clarets’ line-up, with Matej Vydra, Aaron Lennon and Ashley Westwood all returning to starting duty.
Jack Cork’s ankle injury ended his ever-present run in the Premier League since his Turf Moor return at the start of last season.
And the new-look line-up got off to the worst possible start with a self-inflicted wound after just 10 minutes to gift West Ham the lead.
James Tarkowski’s lethargy in possession and mis-hit back-pass allowed Marko Arnautovic a clear run on goal and the Hammers’ returning top scorer made no mistake in slotting the ball past former team-mate Joe Hart.
Hart’s stay at the London Stadium last season was not a particularly happy one but the England international reminded the home supporters of his credentials with a fantastic block to deny the talismanic Arnautovic 10 minutes later.
A second goal then might have made it a long afternoon for the Clarets, who continued to live dangerously for most of the opening half.
Another mis-placed pass, this time from Westwood, ended with a chance for Anderson which would have brought a certain goal but for a miraculous headed clearance on the run from Ben Mee as the Brazilian international bent a shot towards the top corner.
The Clarets then had slice of good fortune when Steven Defour appeared to catch Grady Diangana in the penalty area with an outstretched leg as the Hammers continued to threaten.
But having managed to stay in the game, Burnley got themselves level just before the break.
This time the quality of Westwood’s passing was shown to good affect as he threaded the ball through for Gudmundsson, whose perfectly timed run took him in behind the Hammers’ defence for a deft finish clipped past the advancing Lukasz Fabianski.
No keepers in the Premier League had made more saves this season than West Ham’s number one and Hart.
And it was Hart who continued to rack up the stops either side of half-time with flying efforts to keep out long-range strikes from Pedro Obiang and Arnautovic.
Hart’s contribution kept the Clarets in the hunt and Dyche’s men made a positive start to the second half as they looked to punish the Hammers’ failure to take a firmer grip.
But Burnley’s best spell didn’t throw up another chance and half way through the second period Hart was finally beaten again as the Hammers regained the lead.
Arnautovic and Diangana worked the opening for Anderson, who this time shot low and managed to squeeze the ball through Hart’s legs and into the bottom corner.
Dyche responded by sending on Wood and Ashley Barnes – the goalscorers in the Clarets’ remarkable win here in March – and the move again paid off as Wood rose to power home a header from a corner from fellow substitute Robbie Brady.
But the drama hadn’t finished there and with seven minutes to go the Hammers went back in front again.
Anderson had just been guilty of a bad miss when he curled a shot wide after being set up by Arnautovic.
But luck was on his side moments later when the same combination worked again for Anderson to send a deflected shot looping over Hart via the boot of the luckless Mee, who had given everything for the cause.
In a wide-open contest, the Clarets responded again with Wood only inches away from replicating his double here last season.
But following a surging run and cross from Charlie Taylor, the striker’s header skimmed the top of crossbar.
And in stoppage time the Hammers pounced for a final time to finally secure the points.
Having to gamble everything, Burnley were again caught out on the break, substitute Javier Hernandez providing the finish to another eventful afternoon in Stratford as Burnley’s goals-against column took another hit.
West Ham: Fabianski; Zabaleta, Balbuena, Diop, Cresswell; Obiang (Hernandez 61), Rice, Felipe Anderson, Diangana (Antonio 86); Arnautovic (Ogbonna 90). Substitutes: Adrian, Fredericks, Masuake, Perez, Antonio.
Burnley: Hart; Lowton, Tarkowski, Mee, Taylor; Gudmundsson, Westwood, Defour, Lennon (Brady 75); Vydra (Barnes 72), Vokes (Wood 72). Substitutes: Heaton, Long, McNeil, Hendrick.
Booked: Tarkowski, Lowton, Brady, Barnes.
Referee: Roger East