Neil Danns's 16th-minute goal gave Leicester the points and extended Derby's winless streak to seven games.
Lloyd Dyer produced a sweeping cross from the left wing that was met by Danns's perfect volley at the far post.
Leicester dominated the first half and could have been further ahead at the interval, but Derby improved in the second half.
However, they were unable to find a way through as Leicester's win lifts them to 12th in the table.
Dyer also hit the woodwork twice on a night of one-way traffic after Derby's Nathan Tyson had brought a save from Kaspar Schmeichel after 15 seconds.
Goalkeeper Frankie Fielding was Derby's best player and kept the hosts in the game. After Danns opened the scoring, Fielding twice produced saves to rob him of a hat-trick.
The former Blackburn keeper also thwarted David Nugent in the second half, pushing the former England striker's header on to the bar.
His efforts were in vain, however, as his team-mates failed to take advantage of a close finish and are now without a goal in their last four games.
Leicester have now won six of their last nine games in all competitions and are only eight points adrift of the Championship play-off positions.