After signing new contracts to extend their stays at Turf Moor, strike duo Ashley Barnes and Chris Wood scored the goals that condemned West Ham to a fourth defeat in five in the Premier League.
Barnes ended a run of seven games without a goal in the 11th minute when turning James Tarkowski's header home from close range.
The opener was born from a rather fortuitous corner - with replays showing that Phil Bardsley's attempt had, in fact, taken a touch off Barnes on its way wide.
However, Dwight McNeil's set-piece dropped beyond Roberto Jimenez - who had opted to punch rather than gather a previous delivery from the winger just seconds earlier - and Barnes capitalised.
The Spanish goalkeeper, who hadn't kept a clean sheet in seven appearances going in to this fixture, saved from McNeil and Jeff Hendrick afterwards and he then had a helping hand from VAR as the hosts were denied a second.
McNeil's cross was magnificent, taking Roberto and Issa Diop out of the equation, and Wood powered a header in to the top corner.
Kevin Friend conferred with official Lee Mason for a matter of minutes before a decision was made to chalk the goal off with the New Zealander marginally offside.
Burnley boss Sean Dyche instructed his players to keep their heads from the touchline and they did just that.
McNeil robbed Fabian Balbuena of the ball and rolled it across to Wood who fired past Roberto first time.
There was no reason to consult the Video Assistant Referee on this occasion, though the goalscorer and Hendrick had a quick glance at the big screen just in case.
Burnley were rampant after the break and deservedly extended their lead after Nick Pope had saved from substitute Andriy Yarmolenko and Sebastien Haller.
The third goal was as calamitous as the Hammers' performance. Roberto was unchallenged when Ashley Westwood whipped in the corner and somehow diverted the ball in to his own net. Another VAR check ensued, but Roberto's blushes weren't going to be spared.
A strong hand from Pope kept Aaron Cresswell out, but the action soon swung back round to Roberto's end of the pitch.
The former Olympiakos stopper redeemed himself to an extent after the hour, though it was too little too late by that point.
The 33-year-old denied Wood a second at the near post, he got across well to flick Phil Bardsley's piledriver wide and reacted well to push another effort from Wood over the bar.
Skipper Ben Mee's header was wiped out as Roberto's route to the ball was impeded by Barnes and moments later, when back to his feet, he produced the save of the match when tipping Hendrick's shot over.