Burnley, who had not won in their previous 12 League games, had much the better of the opening 45 minutes but had nothing to show for their endeavours in front of goal.
James O'Connor should have put the home side in front as Chris McCann's far post header from a Wade Elliott cross fell to the on-rushing O'Connor eight yards from goal but the ball bounced off his chest and was cleared.
Leicester's first real threat arrived after 25 minutes with on-loan striker Geoff Horsfield finding Iain Hume whose shot brought a fingertip save from Danny Coyne.
Burnley's nervousness in front of goal was well illustrated when Ade Akinbiyi's pull-back found Joey Gudjonsson at the edge of the box and his shot was turned over from close range by leading scorer Andy Gray.
O'Connor again made his presence felt in the box as he headed over a Gray cross from the left.
Clarets skipper Steve Caldwell was the next player to miss a golden opportunity, heading wide from six yards following a free-kick from Gudjonsson.
With half-time approaching the home side still had nothing to show for their pressure as McCann fired narrowly wide from the edge of the box.
The second half began in similar fashion with O'Connor shooting wide from 20 yards.
Hume was proving to be Leicester's only real threat with a strike from 25 yards which forced a save from Coyne. It was a surprise therefore when he was replaced by Elvis Hammond.
Hammond almost had an immediate impact, sent clear of the Burnley defence, he was denied by a great save from Coyne.
Burnley fell behind in comical circumstances as Caldwell tried to clear but only succeeded in deflecting the ball against fellow central defender McGreal and into the back of the net.
Burnley manager Steve Cotterill responded with a double substitution and one of them, Kyle Lafferty, almost equalised straightaway. But it was not to be for the home side that are now nervously looking over their shoulder at the bottom three.
For Leicester's new owner Milan Mandaric this was a second successive victory and a second clean sheet has brought a maximum return to his new reign at the Walkers Stadium.