Substitute Sam Vokes hit a dramatic late winner to give the Clarets a fifth successive Premier League victory and leave defending champions Leicester still waiting for a first away win of the season.
Vokes volleyed home his seventh goal of the campaign following an 87th-minute corner as Burnley made it seven wins in a row in all competitions at Turf Moor to climb back into the league's top 10.
And Sean Dyche's side continues to make its mark on club history as they became the first Burnley side to win five top-flight games in a row since 1966 on another red-letter day for the club.
Having secured the signings of club record buy Robbie Brady and new midfield colleague Ashley Westwood, the Clarets also looked to maintain their progress on the pitch .
History was not on their side, having failed to beat the Foxes in 10 attempts and losing on Leicester's last three visits to Turf Moor.
But Dyche's enviable crop of players has made a habit of upsetting the form book this season and did it again with another dominant performance which almost refused to yield anything but maximum points.
With Brady and Westwood both watching from the stands, Joey Barton was handed his first Premier League start since returning to Burnley as he lined up in central midfield alongside birthday boy Jeff Hendrick.
And it was the impressive Barton who went closest to opening the scoring in a feisty first half as he looked completely at ease on his top-flight return.
Barton sent a long-range effort over the crossbar and then three minutes before half-time saw a deflected volley dip just over the top as the Clarets stepped up the pressure just before the break.
Leicester's defence was at full stretch as Ashley Barnes and Andre Gray threatened to find a way through on a number of occasions, Barnes clashing with City defender Danny Simpson after claiming a penalty for a pull by the Foxes man.
But it was Gray who had the clearest sight of goal, albeit from a tight angle, after he gave Wes Morgan the slip before striding on to shoot into the side netting.
The champions had failed to score in their previous three games and again found chances hard to come by against a Burnley back four again underpinned by the central defensive fulcrum of former Leicester loan duo Michael Keane and Ben Mee.
Jamie Vardy's only league goals since September had come with a hat-trick against Manchester City in December and the England striker's only opening before the break saw him fail to worry the target from the tightest of angles after intercepting a Matt Lowton back-pass.
With the initiative going Burnley's way, they continued to press at the start of the second half.
Barton and Scott Arfield, who had replaced the injured Steven Defour, both skidded efforts wide and Gray forced Kasper Schmeichel into a decent save low to his left after running onto a Barnes' knock-down to hit a fierce drive towards the bottom corner.
But the Clarets were given a major scare with 55 minutes gone when Leicester should have ended their drought and gone in front as they tried to end a 13-match winless away run.
In a throwback to last season, the Foxes broke dangerously through Riyad Mahrez. His shot was spilled by Tom Heaton and under pressure from the recovering Clarets' keeper, Vardy failed to make good contact when a better touch would have seen him tuck away the rebound.
Burnley countered with Keane and Gray seeing shots blocked following back-to-back corners and Hendrick also had an effort charged down as Leicester defended for their lives.
Gray continued to cause problems and after he forced another corner, the un-marked Mee headed over the top before Gray went it alone and was denied only by Schmeichel's excellent smothering stop.
Burnley continued to knock on the door with Vokes volleying onto the roof of the net with his first touch after replacing Barnes.
And the growing pressure finally told as the Turf Moor crowd urged Burnley on and once again they responded in decisive style.
From a 10th corner of the game Keane broke the shackles of a wall of blue shirts to win a downward header.
The ball bounced up to hit the arm of Vokes but referee Mike Dean was unmoved and the in-form striker crashed the ball into the roof of the net to make it three goals in four games as Leicester went the same way as Manchester United and Manchester City as defending Premier League champions to come unstuck at Turf Moor.
Burnley: Heaton, Lowton, Keane, Mee, Ward, Boyd, Barton, Hendrick (Tarkowski 88), Defour (Arfield 34), Barnes (Vokes 78), Gray. Substitutes: Robinson, Darikwa, Gudmundsson, Flanagan.
Leicester: Schmeichel, Simpson, Morgan, Huth, Fuchs, Drinkwater, Ndidi, Mahrez, Gray (Musa 66), Albrighton (Okazaki 77), Vardy. Substitutes: Chilwell, King, Zieler, Mendy, Benalouane.
Referee: Mike Dean