Former England strikers David Nugent and Darius Vassell struck in the first half and Jeffery Schlupp and Lloyd Dyer scored late-on in the 100th competitive meeting between the two sides.
The hosts had failed to score in their last two outings, but had the ball in the net three times within the first 45 minutes, with Nugent having a second effort ruled out.
The former Portsmouth striker, returning from a hamstring injury, raced clear and slotted home to break the deadlock in the 21st minute.
The forward had another goal ruled out for handball but moments later Vassell blasted home after Neil Danns had struck a post to double Leicester's advantage.
Schlupp and Dyer came off the substitutes' bench to round off the victory and the win meant the Foxes extended their unbeaten run to seven games, while Derby missed the chance to move level with the Championship's table-toppers Southampton.
The Foxes flew out of the traps and had a flurry of half-chances inside the game's opening 10 minutes. Nugent, who had missed the previous four games with a hamstring strain, dragged the game's first chance wide but shrugged off the rust by the time his second chance came around in the 21st minute. Vassell chested the ball down to Gelson Fernandes and, with Derby's defensive line pushed up to the halfway line, he lofted the ball through to release Nugent. The former Preston hitman ran through and kept his composure to slide the ball past Rams goalkeeper Frankie Fielding.
Derby were offering little in attack but did come close when Ben Davies whipped in a cross which narrowly eluded Theo Robinson and Steve Davies.
The Foxes had the ball in the net three minutes before half-time when Nugent stretched to prod home Andy King's drilled cross. But the ball struck the striker's hand and referee Howard Webb disallowed the goal on the advice of his linesman.
What could have been a controversial moment proved to be little more than a footnote when Vassell slammed the ball home moments later. Danns angled a shot across the goalkeeper and when it bounced back off a post, Vassell was on hand to lash in a simple chance.
Nigel Clough's side enjoyed more possession at the start of the second period but Robinson was unable to apply a finishing touch to Gareth Roberts' cross before Leicester goalkeeper Kasper Schmeichel held onto Jamie Ward's drive.
Both goalscorers were substituted and it was Nugent's replacement, Schlupp, who got the third in the 88th minute, sweeping a scuffed volley over the line from a corner.
There was still time for Dyer to squeeze one through Fielding's legs to heap more misery on Derby.