Missing several players through a mix of injuries and suspensions, Burnley managed to stop the rot after three successive defeats but Steve Cotterill's side really should have taken maximum reward.
Leicester, who travel ten miles up the M65 to tackle Blackburn Rovers in the Cup quarter-finals on Saturday, were fortunate to escape with a draw.
Clarets striker Ian Moore was the main culprit early on, his nightmare evening starting inside the first minute when he was clean through on goal only to allow Ian Walker to save.
Leicester survived a real scare when Nikos Dabizas pulled off a dramatic goal-line clearance to keep out an effort from former Foxes defender Frank Sinclair.
The visitors, without a win in six outings and still too close for comfort to the Championship relegation zone, were the better side in the second half and Gareth Williams went close with a good effort.
David Connolly should have done better when clean through but chipped his effort over the top.
Inspired by another all-action performance from midfielder Micah Hyde, Burnley too had their moments and the best chance of the game fell to midfielder John Oster who watched his shot beat Walker only to strike a post.
Graham Branch also went close in the dying stages, but it was to prove yet another blank for the shot-shy Clarets, who managed just a solitary attempt at the City goal and have now failed to score in their last three league fixtures.
Branch had a hat-trick of chances, the best coming in the closing minutes when he somehow managed to head a Michael Duff cross over the bar from close range.
All in all it was fairly mediocre fare for the Turf Moor faithful and the result achieves little for either side - Leicester stay deep in trouble and Burnley still require a couple of wins to be sure of survival.