Leicester believed Elvis Hammond had equalised in the 85th minute when he rolled the ball into an empty net after goalkeeper Stephen Bywater had collided with Richard Stearman.
But assistant referee Carl Bassindale raised his flag for a handball against Stearman and City were adamant they should have been awarded a goal or at least a penalty kick.
Instead it was Derby's day with Sunderland's on-loan striker Jon Stead winning the contest with his first goal in a home game for 30 months.
Stead's precision finish from just inside the penalty area in the 53rd minute was one of the few moments of quality in a poor game, but Derby are currently riding on a wave of confidence and belief.
They did not play particularly well but the breaks are going their way and as long as Stead and fellow striker Steve Howard accept their chances, they will stay in the chase for promotion.
Leicester looked well short of a team capable of mounting a challenge and although they may have been unlucky to be denied an equaliser, the team is short of genuine class.
Derby produced some incisive passing early on but the game quickly degenerated into a scrappy affair with both sides giving away possession carelessly.
The visitors would have gone in front but for a block by Dean Leacock to deny Iain Hume and Howard was fortunate not to receive a red card when he caught goalkeeper Conrad Logan near the end of the first half.
Derby got their noses in front early in the second when Giles Barnes sent in a cross from the Leicester left and Patrick Kisnorbo could only divert the ball into the path of Stead who found the bottom right-hand corner with an unstoppable shot.
Leicester made changes and one of them, Hammond, thought he had rescued his team in the 85th minute but the decision went in Derby's favour.
By then, Howard had seen a header cleared off the line and Arturo Lupoli had fired wide after running clear.
Derby could have rued those missed chances if Stephen Hughes' stoppage time drive had not agonisingly cleared the bar with Bywater beaten.