And, with the Foxes shaken from a 2-0 loss to rivals Coventry, a win was vital.
The breakthrough came on 30 minutes when a dreadful defensive error resulted in Darren Purse scoring a freak own goal. City held on to take all three points on the day, dragging themselves up to 17th in the Championship table.
However, Ian Holloways men remain only a few points above the bottom three with only 11 games to go.
City's next test comes on Tuesday night when they host Preston N.E at the Walkers Stadium. The visitors have a game in hand over City and the game is set to be a real six pointer.