The hosts started the game quite brightly, but capitulated in the latter stages of the first-half, with goals from Ashley Westwood and Chris Wood handing them an almost insurmountable task in the second-half; indeed, they had no reply after the break, ultimately huffing and puffing their way to a fateful defeat.
The result sees Fulham remain 18th and means that their immediate relegation to the Championship in their first season back in the top-flight is now sealed. Burnley, meanwhile, climb three places up into 14th, and now have a sixth consecutive season of top flight football to look forward to.
Story of the game
Coming into the match, Fulham manager Scott Parker made two changes to the side that lost to arch rivals Chelsea last weekend. Kenny Tete came in for Ola Aina at right-back, while Aleksandar Mitrovic replaced Josh Maja to lead the line for the hosts.
Visitors Burnley, meanwhile, were unchanged Sean Dyche opting to stick with the 11 that lost to European contenders West Ham United last time out.
There was a fast tempo to the beginning of the match, both teams pressing high and eager to get the ball forward as quickly as possible. Intricate play from Fulham in the 5th minute worked space for Andre-Frank Zambo Anguissa on the edge of the box, but his left-footed shot was caught easily by Nick Pope.
The hosts were probing, as they had to. Anguissa was the arch instigator of most of their good work, on this occasion clipping the ball out to Ivan Cavaleiro on the right edge of the box; the forward volleyed the ball first-time across the face of goal but it just about evaded the reach of Ademola Lookman, who then glanced Antonee Robinson's follow-up cross over the bar.
Burnley, on the other hand, made a tentative start, their best chance of the opening 20 minutes falling to Ben Mee who glanced Dwight McNeil's free-kick straight into the palms of Alphonse Areola.
However, the visitors thought they'd taken the lead just moments later when Wood caressed home Matej Vydra's cut-back, but replays showed the Czech forward had clearly dribbled the ball out of play in the build-up.
Time and again Lookman found himself in good positions on the edge of the box for Fulham, but the Burnley defence were equal to the challenge he presented at each and every turn, putting their bodies on the line and averting the threat almost instantaneously. That was the nature of the match here: two teams desperate for a result, neither willing to surrender anything in their quest to achieve it.
A somewhat scrappy affair witnessed one of its few moments of invention just past the half-hour mark when Charlie Taylor exchanged a slick one-two with McNeil down Burnley's left. The full-back then crossed first time and met the head of Wood, but the striker's goal-bound effort was blocked well by Tosin Adarabioyo with Areola beaten.
Wood then went close again from the resultant header, but a combined effort from a number of Fulham's defenders managed to scramble the ball away.
Burnley had quite literally sparked into life with the flick of a switch, and took the lead with 35 on the clock. Vydra led the counter-attack, latching onto a long-ball and taking it right to the byline before cutting it back for midfielder Westwood darting into the box; he made no mistake from eight yards out, slotting away to score a crucial, crucial goal for the Clarets.
But Burnley kept looking the better team. That long-ball over the top to Vydra nearly proved a masterstroke once again with half-time looming, the striker's first-time half-volley looping agonisingly wide of Areola's left-hand post.
And there was time for one more for the visitors before the referee blew for half-time. Wood finally scored the goal his performance thus far had warranted when he linked up well with Josh Brownhill before crashing home a brilliant finish from the edge of the area, with Areola utterly helpless to resist the effort.
As it stood heading into the break, Fulham were set for an immediate return to the Championship in miserable style. They needed to turn things around, and pronto.
The first 10 minutes of the second half offered nothing by way of encouragement, with Burnley pretty comfortable and the hosts showing a fraction of the urgency needed to turn this game on its head. They were well and truly whimpering their way back down to the second tier.
Fulham's first opening of note following the break came when Lookman's lofted corner met the head of Mitrovic on the penalty spot, but the defender's powerful header was directed straight at Pope with the rest of the goal gaping.
Moments later, Mitrovic glanced Bobby Decordova-Reid's chipped cross into the side netting after a quick breakaway. The hosts were pushing but, thus far, to no avail, and Burnley's lead always felt fairly comfortable.
Fulham were appealing for a spot kick with about 25 minutes remaining when Taylor dived in on Cavaleiro in the box, but both referee Anthony Taylor and VAR agreed that the defender got all of the ball and none of the man in what was nonetheless a fairly risky challenge.
Understandably, Fulham were going all guns blazing, with Burnley happy to sit back and soak up the pressure. The conservatism of the visitors nearly came back to bite them when Lookman cut the ball back for Anguissa on the edge of the penalty area, but the Cameroon international cannoned his vicious effort off the crossbar and James Tarkowski was able to clear.
The hosts had missed a succession of chances to halve their decisive deficit, and they were almost made to pay with 15 minutes when substitute Jay Rodriguez was set through on goal by McNeil, but the striker's first-time effort merely stung the palms of the outrushing Areola.
Nothing was coming off for Fulham. Anguissa their bright spark for most of the match, lashed an effort way high and wide from 35 yards before a header from Ruben Loftus-Cheek trickled out of play far away from Pope's goal. They weren't even threatening to get back into this game. The knowledge that they were now just moments away from relegation was visibly creeping in.
This relegation wasn't for the want of trying to avert it, but in the end Fulham simply weren't good enough. Players bent double at full-time, others sprawled out on the Turf, indicates this is a destiny which really hurts the Craven Cottage contingent — but they must pick themselves up and go again just like they did in 2019/20.
Takeaways from the match
Fulham down, and deservedly so
Remember when Fulham beat champions Liverpool on the famous Anfield turf back in March? Survival felt less a likelihood, more a probability at that point, with the Cottagers in pretty good form heading into the run-in. Oh, how things have changed since then.
They haven't won since and, in a recent run of three games in particular, surrendered six points in the dying stages of matches against Aston Villa, Wolverhampton Wanderers and Arsenal. Those results coupled with this today are what ultimately proved the nail in their coffin.
Nonetheless, the picture's been pretty bleak for Fulham all season. On good days they're easy on the eye, but have never been clinical or resilient enough to make good performances pay dividends. On other days, like this, they simply haven't been up to the standard required for the Premier League — now attentions turn to bouncing straight back like they did last season.
Imperious performance seals Burnley's survival
In many ways, this was Burnley at their finest. They only needed two clear openings to wrench themselves into a good position and relied on their organisation and sturdiness to see the rest of the game out. In many stages of the match, they had Fulham right where they wanted them, Pope's goal remaining unthreatened for the vast majority of proceedings here.
The result seals a sixth consecutive season of Premier League football for Dyche's men, and that is no mean feat. For the time being they can celebrate their achievement, but the time will come when they must focus on what is set to be a tricky and potentially decisive summer at Turf Moor.
Fulham: Areola; Tete (Maja 54'), Andersen, Adarabioyo (Loftus-Cheek 73'), Robinson; Anguissa, Lemina; Cavaleiro, Decordova-Reid (Onomah 65'), Lookman; Mitrovic.
Unused subs: Rodak, Aina, Hector, Ream, Bryan, Carvalho.
Burnley: Pope; Lowton, Tarkowski, Mee, Taylor; Brownhill, Westwood, Cork, McNeil; Vydra (Rodriguez 66'), Wood (Barnes 84').
Unused subs: Peacock-Farrell, Norris, Bardsley, Dunne, Pieters, Stephens, Gudmundsson.
Following their relegation here, Fulham travel down to the south coast to face Southampton on Saturday.
Burnley, meanwhile, host Leeds United in the lunchtime kick-off on the same day.