And, the win leaves City in 13th place (their highest position so far this season after a poor run of games), just four points behind the play off places.
A thunderous volley from Danny Tiatto and a fifth goal of the season for striker Iain Hume secured the points for the Blues.
Andy Welsh made his debut after Gareth Williams limped off injured with a suspected serious ankle injury. Welsh made an immediate impression, knocking the ball into the path of Tiatto for the opener.
Leicester comfortably hung on for all three points despite a late goal from Leeds Captain Butler on 86 minutes.