A late goal from Chris Wood finally laid the West Ham bogey to rest to ease the frustration around Turf Moor and extend the Clarets’ unbeaten run to six games.
The Hammers looked as though they were set to hold out to secure a sixth successive win over Burnley – including five in the Premier League – despite playing for more than an hour with 10 men.
Andy Carroll’s sending off for two bookings in as many minutes had sent the visitors on the defensive as they looked to protect the 19th-minute lead given them by Michail Antonio's gift-wrapped goal.
Chris Wood scores his fourth Burnley goal
But the Clarets’ persistence and never-say-die attitude finally paid off in the 85th-minute when Wood powered home a header to make it three goals in six top-flight appearances for the club’s record signing as Sean Dyche’s men deservedly earned the point which keeps them level on points with heavyweights Chelsea, Arsenal and Liverpool in seventh place in the Premier League.
The Clarets, not surprisingly, were unchanged following their win at Everton before the international break which made it a best top-flight start since 1973.
But in that run, home points have been hard to chisel out and West Ham threatened to make it that way again as they grabbed the initiative after being handed an early opening goal.
Michail Antonio became only the second opposition player to score a Premier League goal at Turf Moor this season
Burnley have rightly prided themselves on their defensive record this season but were badly caught out when goalkeeper Joe Hart launched a long clearance that by-passed the Clarets’ back four and eluded an attempted clearance from Ben Mee to give the speedy Antonio a run at goal.
Nick Pope made a half-block but couldn’t stop Antonio completing the job with a simple tap-in to give the visitors the perfect start to their quest to secure a first away win of the campaign.
The Hammers had come with an attack-minded line-up but seven minutes later were forced into a re-shuffle by Carroll’s red card.
The big striker had just jumped with an arm into the face of James Tarkowski before targeting Ben Mee for another dangerous aerial challenge which brought a second yellow card in as many minutes.
Andy Carroll was booked twice in 99 seconds
That left Chicharito as the visitors’ only attacking outlet as they went on the defensive to try and protect their lead.
The Clarets dominated possession but couldn’t get back on terms before the break.
Robbie Brady, Jeff Hendrick and Steven Defour all threatened from distance after the the impressive Defour had curled a lovely early cross onto the head of Chris Wood, who headed at Hart.
And when Hart and Wood faced off again it was the England international who came out on top – just – as he got the benefit of the doubt from referee Stuart Atwell.
Wood beat Hart to a threaded pass from Brady but Atwell evidently felt the on-loan Manchester City keeper had touched ball before colliding with Wood, awarding a corner rather than a penalty 12 minutes before half-time.
Wood goes down under a challenge from Joe Hart
Dyche then a made a double change at the break as he looked to find a route to goal, sending on Sam Vokes and Iceland World Cup hero Johann Berg Gudmundsson in a switch back to a 4-4-2 formation.
Vokes was immediately involved with a dummy to set up a shooting chance for Wood, which was blocked, while Gudmundsson also added to the attacking threat.
West Ham – who had sent on Pedro Obiang to try and stiffen their resolve in midfield - did carry a threat on the break as Pope was forced to save from Antonio after the visitors’ best move on the match.
But with 63 minutes gone, the Clarets were a whisker away from equalising as Gudmundsson’s low drive beat Hart but hit the foot of the post and bounced back into the keeper, who was relieved not to see it ricochet over the line.
Stephen Defour earned the man-of-the-match award
Having survived that scare, it looked as though the visitors might be able to hold out as they frustrated the Clarets with some dogged defending and spoiling tactics designed to disrupt the game and run down the clock.
Burnley peppered the penalty area and sent on another striker in Ashley Barnes to try and force the break-through as they chased only a second league goal at home this season.
But it looked as though their efforts may prove in vain until Wood emerged as the saviour with five minutes to go.
Gudmundsson provided the touch of class out wide on the right with the perfect delivery and Wood did the rest, rising to nod home his third goal in four games at Turf Moor and give Dyche’s men a suitable reward.
Burnley: Pope, Lowton, Tarkowski, Mee, Ward (Barnes 81), Arfield (Gudmundsson ht), Cork, Defour, Brady, Hendrick (Vokes ht), Wood. Substitutes: Lindegaard, Taylor, Westwood, Long.
Booked: Defour, Wood
West Ham: Hart, Zabaleta, Reid, Fonte, Cresswell, Antonio, Kouyate, Lanzini (Masuaku 87), Arnautovic (Obiang ht), Carroll, Chicharito (Sakho 74). Substitutes: Adrian, Noble, Ayew, Ogbonna.
Booked: Carroll, Obiang, Reid
Sent off: Carroll
Referee: Stuart Attwell