The timid Foxes were ruthlessly torn apart by Marco Silva's men, who stormed into a 3-0 first-half lead thanks to strikes from Willian, Tom Cairney and Carlos Vinicius.
Willian and Cairney completed their braces in the second 45, but Harvey Barnes (2) and James Maddison added to the drama as the Cottagers' defence went to sleep, although there would be no sensational turnaround for those in blue.
Leicester's top-flight safety may have been at stake at Craven Cottage, but Dean Smith's charges played like a side who had already been consigned to the drop during a disastrous opening 20 minutes.
Halfway through that period, Dennis Praet scythed down Antonee Robinson to gift Fulham a free kick, albeit from a position of very little danger on the left-hand side.
However, Willian's inswinging set-piece evaded every outfield player in the box and bounced over the head of a hesitant Daniel Iversen to give the Cottagers the lead in unorthodox circumstances.
One week ago, Iversen was lauded for his performance in the Foxes' draw with Everton, but the Dane was certainly culpable for Willian's freak opener, and the visitors remained on the back foot henceforth.
The Foxes were carved open again in the 18th minute, as the tough-tackling Joao Palhinha won the ball back in midfield before laying off Harry Wilson, who drove into space infield and slipped through Vinicius to coolly find the far corner.
Fulham's two-goal lead was richly deserved, but Leicester belatedly began to show a bit of bite soon after Vinicius's second, as Bernd Leno was forced into a top save from Jamie Vardy in the 20th minute.
Both goalkeepers continued to be peppered with shots, and Iversen somewhat redeemed himself for his earlier error in the 30th minute, thwarting Harrison Reed's close-range effort on the half-hour mark.
However, just when the Foxes may have started to regain a slice of hope, Cairney would seemingly kill the game off in the 44th minute, cutting onto his right foot inside the box and bending a lovely finish into the bottom corner.
The travelling fans' assessment of the opening 45 minutes was summed up by a cacophony of boos, and all Smith could do at half time was introduce Tete in place of Praet to try to inject some life into an ailing side.
One Tete would play a key part in the game's fourth goal, but it was the Leicester attacker's namesake, as Fulham's Kenny Tete picked out the charging run of Cairney into the box, and the Scotsman took a touch before finding the bottom corner for his second of the afternoon in the 51st minute.
Fulham were in cruise control and then some, but there were muted cheers from the away end in the 59th minute, as Maddison stopped Timothy Castagne's cross dead inside the box before teeing up Barnes to curl home off the bar.
It was surely too little too late for Smith's side to launch an extraordinary fightback, but a couple of eyebrows were raised when Leno felled Vardy inside the box, giving Leicester the chance to halve the deficit from 12 yards.
Vardy stepped up and went for placement, but Leno guessed the right way and redeemed himself with a relatively comfortable save, adding to Leicester's penalty disasters following Maddison's missed spot kick against Everton last week.
With that miss, Leicester's confidence only depleted further, and Willian joined Cairney in the two-goal club in the 70th minute, curling a sumptuous strike into the bottom corner from 25 yards.
The goal-happy hosts were still in a charitable mood, though, and Palhinha offered Maddison the chance to exorcise his penalty demons by bringing down the Leicester man inside the area - the Englishman went for the same corner as Vardy, but Leno sprung the other way as the Foxes pulled another goal back in the 82nd minute.
Another defensive calamity from Fulham allowed Barnes to double his tally in the 90th minute, as the Englishman slotted home following a mix-up between Leno and Shane Duffy, but six minutes of added time was not enough for Smith's side to save their bacon.
The Foxes remain 16th on 30 points for the time being, but should Everton beat Brighton & Hove Albion and Nottingham Forest take at least a point away from their meeting with Southampton, Smith's side could end the day in the relegation zone.
Leicester now prepare to host Liverpool in their penultimate home game of the season next Monday, while Fulham - who stay 10th - travel to basement side Southampton in five days' time.