The Foxes looked on the ropes from the off as the pace of Ademola Lookman caused them serious problems on the break. Andre-Frank Zambo Anguissa played through the winger with a sublime assist for the opener on half an hour, and and unlikely lead was made even unlikelier when Ivan Cavaleiro doubled it from the spot before the break.
The visitors looked comfortable in the second period and coped with everything Brendan Rodgers threw at them. Harvey Barnes and Cengiz Under emerged from the bench but couldn't force anything for the most part as Scott Parker's team showed a level of composure that would have delighted the manager.
Barnes did get on the score-sheet late on to set up a nervy finish, but Fulham were good value for their three vital points.
Here are the player ratings.
1. Goalkeeper & Defenders
Kasper Schmeichel (GK) - 6/10 - Had no real chance with either goal and was quiet otherwise.
Wesley Fofana (RCB) - 6/10 - Should have opened the scoring early on and was made to pay for that error by a clinical Fulham performance. The best of Leicester's defenders though that isn't saying too much.
Jonny Evans (CB) - 5/10 - Fairly steady at the heart of the back three though might have been positioned better for the opener. Nearly sold out his keeper with a self-destructive pass at 2-0 but was bailed out by Fofana.
Christian Fuchs (LCB) - 5/10 - Really clumsy to give away the VAR-assisted penalty for the second and that set the tone for a really iffy performance.
2. Midfielders & Wing-Backs
James Justin (RWB) - 6/10 - Seemed lively and tried to get Leicester forward but his final ball wasn't there. Got at Antonee Robinson a few times and looked as likely as anyone to make something happen.
Youri Tielemans (CM) - 6/10 - Was at the heart of most good things Leicester did but struggled to break through the lines like he usually can. Mixed his game up but was given no quarter.
Nampalys Mendy (CM) - 5/10 - A bit slow and ponderous and was bypassed easily for a couple of counter-attacks. Rarely had the ambition to move play forward though that isn't really his game.
Luke Thomas (LWB) - 5/10 - Fairly quiet and ineffectual before being withdrawn at the break.
Dennis Praet (RW) - 5/10 - Didn't really look at home off the right of Jamie Vardy before he was taken off at half-time.
Jamie Vardy (CF) - 6/10 - Leicester so rarely got the ball to him and his few attempts to drop deep to get on it came to nothing. Showed his influence in flashes but was largely frustrated by his team-mates' lack of cutting edge.
James Maddison (LW) - 6/10 - His form has gone off a cliff this season and you could see why as he struggled to impose himself.
Harvey Barnes - 6/10 - Scored and looked lively, but it was too little, too late
Cengiz Under - 6/10
Kelechi Iheanacho - 6/10
5. Goalkeeper & Defenders
Alphonse Areola (GK) - 7/10 - Met everything he was faced with well though he might have expected a busier afternoon at the King Power.
Ola Aina (RCB) - 6/10 - Looked strangely at home in the back three and popped up with a couple of big aerial clearances to relieve the pressure from his side.
Joachim Andersen (CB) - 7/10 -Probably his best game in a Fulham shirt as he held things together admirable in the middle of a thrown together defence.
Tosin Aradibioyo (LCB) - 6/10 - Was tasked with bringing the ball out from the back and looked a little unsure of himself but otherwise steady.
6. Midfielders & Wing-Backs
Bobby Decordova-Reid (RWB) - 6/10 - Seemed a strange decision to start him as a wing-back but he seemed comfortable in the new role.
Harrison Reed (CM) - 6/10 - Sat between the lines and broke up play well without pulling up any trees.
Andre-Frank Zambo Anguissa (CM) - 7/10 - The renaissance of Fulham's one man engine continues apace. Sublime assist for the opener as he led the counter-attack by himself.
Antonee Robinson (LWB) - 7/10 - Supported Fulham's few ventures forward with his dynamic movement and was solid defensively even after Leicester's second-half reinforcements.
Ruben Loftus-Cheek (RW) - 5/10 - Was clearly out of position playing off the front three and struggled to really get into the game before his withdrawal.
Ivan Cavaleiro (CF) - 6/10 - Fell on his backside the last time he tried to take a penalty but absolutely no danger of that here as he comprehensively thumped the ball into the top corner. As makeshifts centre-forwards go he looks just about adequate.
Ademola Lookman (LW) - 8/10 - Great composed finish for the opener with no inexplicable attempt to chip the ball down the middle in sight. If Fulham stand any chance of staying up this season, he's it.
Mario Lemina - 6/10
Aleksandar Mitrovic - 4/10
Joe Bryan - N/A