David Nugent's expert finish after a clever shimmy gave Leicester the advantage in the first half as both sides seemed reluctant to give too much away in their continued search for Premier League football next season.
Burnley had their chances to respond but paid for their lack of firepower up front, with Sam Vokes joining Danny Ings on the sidelines with injury in the first half and Ashley Barnes forced to lead the line on his own.
Chris Wood made Burnley pay for their profligacy in the closing stages with a stunning strike, securing a vital win for Leicester - and inflicting the Clarets' first league defeat on home soil this season.
Both sides came into the game in excellent form, with second-placed Burnley 10 points clear of third-placed QPR in the race for one of the two automatic promotion spots, and Leicester a further three clear of their hosts.
With the two unbeaten since December - Burnley since Boxing Day and Leicester since December 7th - the expectations of a tough, close match between two excellent and well-organised sides were certainly well-founded.
The first half threatened to pass by without incident, as Leicester's creative lynchpins in Anthony Knockaert and Riyad Mahrez were largely thwarted by Burnley's fierce backline.
With Ings already sidelined through injury, Burnley were to suffer another blow just eight minutes into the game as Vokes hobbled off with a knee problem.
Burnley had the next chance on 17 minutes after Jeff Schlupp's sloppy play in his own half gave Barnes the chance to find Michael Kightly's unmarked run on the right, but Foxes captain Wes Morgan was across instantly to clear the danger.
As both sides swapped possession throughout the game, Leicester's first real opening came on 25 minutes when Ritchie De Laet's searching cross found the head of Jamie Vardy, whose flick-on just evaded the onrushing Mahrez.
Just two minutes later it was Vardy again at the centre of the action, capitalising on Michael Duff's mistake to burst through into the penalty area, and though Burnley recovered well to clear, Vardy's calls for a penalty amidst Jason Shackell's tussling fell on deaf ears.
That turned out to be Vardy's last action, as he left the field on 34 minutes due to a knock, and was replaced by Leicester's midweek hero Wood.
Just a minute after coming on Wood proved the difference, running directly through the Burnley defence before holding the ball up for Nugent, who calmly sold Duff a dummy before curling past Tom Heaton with ease.
The goal sparked Burnley into life as Barnes and Kightly swapped chances, before David Jones' header from a corner led to a double penalty shout for handball, which referee Chris Foy again rejected.
Leicester were quickest out of the blocks in the second half as Knockaert's stunning 20-yard drive rebounded back off the crossbar after 50 minutes.
The hosts should have equalised just one minute later however, when an uncharacteristic slip from Morgan gave Arfield a chance to shoot in the area, but Kasper Schmeichel closed the angle and saved well.
The Foxes should have put the game beyond doubt on 67 minutes when Schlupp found space wide on the right before cutting in and firing a low cross. The cross rebounded back to him however before he unleashed a rasping effort, which was blocked on the line by Shackell.
Kightly then fired in a powerful effort 10 minutes later as Burnley chased an equaliser, but Schmeichel was again equal to it.
But Leicester's strength in depth showed once more just one minute later when Knockaert's long punt upfield found Wood, who looped the ball over Heaton with a great effort to round proceedings off.