The Clarets left themselves with a mountain to climb to reach the play-off places after getting a mauling in the Foxes' den.
Three second-half goals put this on a par with Burnley's heaviest Championship defeat of the season as Leicester leap-frogged Eddie Howe's men in the race for a top-six finish.
Former Blackburn Rovers forward Paul Gallagher helped himself to a double, including one from the penalty spot, as Sven Goran Eriksson's big spenders turned on the style.
The Clarets had no answer as their winless run stretched to five games and left them facing a seemingly must-win game at Nottingham Forest on Tuesday night to revive their fading promotion hopes.
Howe's efforts to rediscover a winning formula had brought more changes with Brian Jensen, Michael Duff, Wade Elliott and Chris Iwelumo all returning to starting duty.
Jensen was back in goal for the first time since October in a bid to help shore up a Clarets' back line which had shipped nine goals in the previous four games.
Nathan Delfouneso leads a rare attack
And the great Dane made a commanding enough start as he came to meet a couple of crosses in a decent enough start for the visitors.
At the other end, Chris Weale was forced to go full length to turn a Nathan Delfouneso drive around the post and Chris Eagles also saw a shot blocked in front of goal by Patrick Van Aanholt following a corner.
But the Foxes started to find their passing game and Jensen was picking the ball out of the net mid-way through the opening half.
Top scorer Andy King had twice mis-kicked in good positions but Diomansy Kamara was not about to pass up the next opportunity on his home debut.
The on-loan Fulham forward looked Premier League class all afternoon and when fellow loanee Yakubu forced his way into the box, the Senegal international pounced to take the ball off his toe and make no mistake with a low shot past Jensen and into the bottom corner.
The goal was the cue for Leicester to take a grip with some silky football in the sunshine but the Clarets at least dug in to stay just one goal adrift at the break.
Chris Eagles puts Chris Weale under pressure
And when Tyrone Mears had a half-chance a minute into the second half the prospect of a comeback was on the cards.
A fine run and cross from Delfouneso saw Weale drop the ball in the penalty area but it landed at an awkward height for Mears, whose attempted volley under pressure went well over the top.
The Clarets needed to try and build on that momentum but after 50 minutes they went 2-0 down and the game was effectively up.
Kamara was again instrumental as he linked play on the edge of the penalty area and when he ran into the box to meet a pass from Gallagher, his tumble from Andre Bikey's trip saw Mike Dean point to the spot.
Gallagher did the rest as his driven penalty just squeezed under Jensen's dive to give him his tenth goal of the season.
Kamara then threaded Yakubu through for a run on goal which required an excellent last-gasp tackle from Duff to deny the Everton man the chance of a third.
Andre Bikey trips Diomansy Kamara and it's a penalty
Bikey tried to make amends with a header over the bar from an Elliott free-kick and a fine block from King in front of his own as the Foxes looked to press home their superiority.
But no-one in a white shirt got near Gallagher as he made it 3-0 with 20 minutes to go with a 30-yard drive which flew past Jensen into the corner of the net.
Howe responded by sending on Steven Thompson on his return from injury and Ross Wallace to try and rescue something from the afternoon.
But with Eriksson doing likewise with Steven Howard and former England international Darius Vassell to underline the depth of the Foxes' attacking resources, Burnley had to give way to another side displaying its belated top-six credentials.
Frustrating day for the fans
Eriksson's side had won only one of their previous seven games but they ended that run in style as Patrick Van Aanholt scored the goal of the game as he rounded off another superb passing move with a magnificent curling finish.
That was enough to equal the margin of the Clarets' home defeat to Reading in October as a previously unbeaten record at the Walkers Stadium was written off.
And it could have been worse as Richie Wellens volleyed against the bar and only Jensen's finger-tip save prevented Gallagher completing his hat-trick five minutes from the end of a sobering afternoon.
Burnley: Jensen, Mears, Duff, Bikey, Easton, Marney, Elliott (Wallace 73), Eagles, Delfouneso, Iwelumo (Thompson 73), Rodriguez (Alexander 86). Subs: Carlisle, Duffy, Edgar, Grant.
Booked: Marney 25, Rodriguez 40, Bikey 51
Leicester: Weale, Van Aan Holt, Vitor, Bamba, Mee, Oakley (Abe 79), King, Wellens, Gallagher, Yakubu (Howard 73), Kamara (Vassell 73). Subs: Teixeira, Howard, Dyer, Berner, Abe, Ricardo.
Referee: Mike Dean