On day of mayhem at the London Stadium, the Clarets inflicted damage of their own with a superb second-half performance to secure an emphatic first away win since November.
Two goals from substitute Chris Wood and a stunning opener from Ashley Barnes earned the Clarets a fifth away win of the campaign and a new record Premier League points’ total.
Having hit the 40-point mark a week earlier, Sean Dyche’s immediately men kicked on to keep a firm grip on seventh place.
But it was a bleak day for West Ham, who suffered a third successive defeat by a three-goal margin for the first time in a decade to stay in relegation danger.
And more disturbingly, fans came onto the pitch after the first two Burnley goals, approaching players without obstruction and forcing Hammers’ captain Mark Noble and defender James Collins to take matter into their own hands to try and restore order.
Protesting fans also massed around the directors’ seats and dug-outs as they vented their anger.
But the Clarets kept their composure impeccably and among the chaos, Wood tucked away a late third goal as Burnley made it a treble for the first time since their opening day win in the capital at Chelsea.
The Hammers had started the afternoon with a look back to happier times as they marked the 25th anniversary of the death of club legend and former England World Cup-winning captain Bobby Moore with the laying of a wreath and a minute’s applause before kick-off.
It was then a current England international who took centre stage as goalkeeper Joe Hart was handed his first Premier League start by the Hammers since November.
With the World Cup finals around the corner it was a timely return for Hart’s hopes of making it to Russia.
But in truth he had little chance to impress during a first half in which Nick Pope was the one to press his international credentials.
The Clarets’ keeper has been mentioned as a candidate to make Gareth Southgate’s squad for their up-coming friendlies when it is announced next Thursday.
And he again did his cause no harm in a stop-start opening period devoid of any pattern but which did bring chances for a West Ham side struggling to stay clear of the drop-zone, but which is unbeaten at home this year.
The first fell to Marko Arnautovic after he was played in by on-loan Inter Milan forward Joao Mario but Pope reacted well to keep out his angled drive with his legs.
Manuel Lanzini then curled an effort over the bar before Mario sent a volley too high after Pope had been blocked off as he tried to come and claim a corner.
And Pope then made another crucial stop to keep the scores level at the break when he stuck out a leg to deny Lanzini after Angelo Ogbonna’s header over the top had released the Argentina international.
The Clarets had played only in patches before the break but started the second half in positive fashion with Stephen Ward making a couple of excellent forward runs, from the second picking out Barnes to shoot past Hart from a position only inches off-side.
And with an hour gone, Dyche made the switch which had proved so effective in beating Everton a week ago by sending on Wood to partner Barnes in attack.
The pair made an immediate impact with a one-two between the duo ending with Barnes shooting just wide from 25 yards.
But that was nothing compared with their link-up moments later as the Clarets grabbed the lead in spectacular style with 65 minutes gone.
Wood’s run into the channel was detected by Lowton who played a perfect pass in behind the West Ham defence.
Wood held the ball up before playing a perfect pass into the stride of Barnes, whose thundering finish gave Hart no chance as the in-form striker scored for the third successive time since 2011 in front of watching Austria boss Franco Foda.
The re-start was delayed as a small handful of West Ham supporters came onto the pitch.
And as protests began to ring around the stadium, the Clarets kept their nerve to quickly go 2-0 up.
Again Barnes was involved, poking the ball out to Aaron Lennon whose low cross was steered home by Wood as he quickly joined his strike partner on seven goals for the campaign.
More unrest added to an ugly feel inside the stadium as supporters displayed their frustration at the club’s board and the team’s current position.
But the Clarets admirably kept their concentration and eight minutes from time added a third to complete their biggest win of the season.
And again it was the predatory Wood who struck, following up to tuck the ball away after Hart had failed to hold a shot from Johann Berg Gudmundsson.
On a poor day for football, the Clarets at least did their job in exemplary fashion.
Burnley: Pope, Lowton, Tarkowski, Mee, Ward, Lennon, Westwood, Cork, Gudmundsson, Hendrick (Wood 60), Barnes (Vokes 89). Substitutes: Lindegaard, Nkoudou, Marney, Vokes, Bardsley, Long.
West Ham: Hart, Zabaleta, Collins, Ogbonna, Cresswell, Noble, Kouyate, Mario (Hernandez 71), Arnautovic, Antonio, Lanzini. Substitutes: Adrian, Hugill, Hernandez, Evra, Cullen, Rice, Browne.
Referee: Lee Mason