Late goals from Paul Dickov and sub Trevor Benjamin secured the points for the Foxes who could even afford to concede an injury-time own goal from Frank Sinclair.
But Burnley could point to a series of missed chances long before the visitors nudged in front.
Robbie Blake, otherwise outstanding, managed to miss four clear cut chances as the visitors goal enjoyed a charmed life.
And how Burnley were made to pay for their failure to test Ian Walker when Dickov bundled home a corner from the left from Muzzy Izzet 11 minutes from time.
Burnley keeper Marlon Beresford might have done better and that was certainly the case five minutes later when Leicester made sure of the points with a second.
Again it followed an Izzet corner from the left and further indecision from Beresford allowed Benjamin to power home a close-range header.
Burnley had late hope when Sinclair turned a cross from Glen Little past his own keeper but Leicester hung on to move within two points of Portsmouth.