The Foxes could have slipped into the bottom three with a defeat but they extended their unbeaten run to four games thanks to strikes in either half from Andy King and Steven Howard.
Darius Vassell had a goal disallowed before King broke the deadlock with a calm finish after he had ran on to Richie Wellens' pass.
Derby had opportunities to equalise though, with Paul Green particularly culpable as his unmarked header missed the target.
Howard wrapped up the points when he netted from the penalty spot after Kyle Naughton was fouled by Kris Commons in the area.
The result sees Leicester move five points clear of the relegation zone whilst promotion-chasing Derby slipped eight points behind second-placed QPR.
Following a tentative opening, Vassell thought he had scored his first goal for Leicester when he latched on to Greg Cunningham's long-range pass and finished past Frank Fielding, however, the former England international was flagged offside.
The Foxes did take a deserved lead in the 13th minute though thanks to King.
The midfielder latched on to Richie Wellens' through ball and expertly placed the ball past Fielding to register his seventh goal of the season.
Leicester were making a mockery of their league position and Howard nearly put them two goals to the good immediately after but he headed over from Naughton's cross.
Derby though were unbeaten in six matches against Sven-Goran Eriksson's men and Commons was a menace to the Leicester defence, however, he was unable to trouble Chris Weale with his two long-range efforts.
Howard had two further chances to extend Leicester's lead after the interval but he missed the target on both occasions.
The former Derby man headed over from Vassell's cross and although his 20-yard strike look destined for the net, it missed the post by a matter of inches.
The veteran striker should have been made to rue his misses as Paul Green spurned a glorious chance to grab a leveller for the Rams.
Moore's left-wing cross found the midfielder at the back post but Green, who was given acres of space, headed wide.
Lloyd Dyer replaced Vassell in the 64th minute and his introduction caused no end of problems for Nigel Clough's men.
The substitute shook off the challenges of several Rams defenders and unleashed a shot from just inside the area which produced a magnificent save from Fielding.
Wellens and Dyer linked up to release Naughton on the right channel and just as the defender had brought the ball into the box, he was brought down by Commons.
Referee Steve Tanner had no hesitation in awarding a penalty and Howard grabbed the goal his performance deserved by coolly slotting home.
Paul Gallagher nearly added to the Foxes euphoria in injury-time, however, his strike from 12 yards was well saved by Fielding.