Foxes manager surprisingly left England international Ben Chillwell on the bench as Christian Fuchs was handed a start at left-back, although they were without Wilfried Ndidi.
It was evenly contested affair in the early exchanges, although both sides struggled to carve out clear-cut chances in the opening 20 minutes.
Leiecester eventually broke the deadlock in the 33rd minute as Harvey Barnes skipped past two Burnley defenders before rifling the ball past Burnley goalkeeper Nick Pope.
Unfortunately, that proved to be the half only bit of goal-mouth action as Sean Dyche's charges failed to trouble Kasper Schmeichel with any serious attempts in the latter stages of the half.
Burnley got themselves back into the contest after 56 minutes when Chris Wood showed reactions turn home Ben Mee's header, much to the delight of the home crowd.
The Foxes were then awarded a penalty with 20 minutes reamining following Mee's foul on Barnes, but Jamie Vardy saw his spot-kick saved by Pope.
The visitors were made to rue that miss as Burnley took the lead on 79 minutes as Jonny Evans' clearance fell to Ashley Westwood, who smashed the ball beyond Schmeichel from close range.