Nigel Pearson's league leaders looked every bit promotion candidates - even title contenders - on Friday night.
Richie De Laet's first goal in just over a year gave them the half-time lead, but the advantage could have been much greater as Jamie Vardy and Liam Moore saw efforts strike the woodwork.
A Nugent double and a deserved goal for Vardy saw Leicester send out a warning to the rest of the division, with the response particularly impressive after Derby had halved their arrears through a De Laet own goal.
The Rams were simply out-played and offered little as they slipped to successive league losses and an eighth defeat in their last nine matches against the Foxes - including a third to Pearson's team this season.
The first chance came after 12 minutes. Neat play between Vardy and Nugent opened up the Derby defence allowing Lloyd Dyer in on goal down the left- hand side.
Dyer's shot was parried back into the centre of the penalty area by Lee Grant and Matty James steered his shot wide with an unguarded net at his mercy.
Leicester began to assert their dominance and Danny Drinkwater, Championship player of the month for December, drilled in a low cross from the left. Vardy dummied the ball and it skidded inches wide of the far post with Grant stranded.
There was a nice piece of skill from Nugent midway through the first half as he teed himself up for a volley but Grant got down well to push the ball behind at the foot of his near post.
Nugent was involved again for the goal after 25 minutes. Leicester's leading scorer played a one-two with De Laet, who fired a left-foot shot into the bottom corner of the net.
It was a good strike by the right-back but the Derby defenders stood off him.
Vardy flicked the ball to Nugent whose 35th-minute effort was saved by Grant. Vardy reacted quickly to the rebound and from a tight angle shaved the crossbar with his effort.
A minute later Leicester hit the bar again through Moore's thumping header from James' corner.
The second goal Pearson's side had been threatening arrived just three minutes after half-time.
Derby failed to deal with Kasper Schmeichel's long clearance and Vardy got in front of former Fox Michael Keane, who during a loan spell last season made 27 appearances for Leicester.
Vardy set up Nugent and his initial shot was blocked by Jake Buxton but the ball ricocheted off the striker and into the net beyond the helpless Grant.
Steve McClaren reacted by bringing on strikers Mason Bennett and Patrick Bamford - a loan arrival this week from Chelsea. Jamie Ward and Simon Dawkins were the men to make way.
The move looked to have worked when after 59 minutes Buxton's header found its way into the back of the net via a flick off De Laet.
But Leicester's response was ruthless, although in the first instance it was aided by a silly challenge from Craig Forsyth.
His needless sliding challenge on Vardy, with the striker heading away from goal, saw referee David Coote point to the penalty spot and Nugent netted his 15th goal of the season.
Then it was four. Derby were torn apart through the middle and Vardy lashed the ball beneath Grant from just inside the area.
With 64 minutes on the clock the game had suddenly been taken away from the Rams.
One-time Derby target Chris Wood, on as a substitute, went close to making it five near the end but his shot went just wide.
The best home record in the Championship prevailed against the best away record and Leicester, deservedly so, left the field to a standing ovation from their supporters after the final whistle - a whistle that must have seemed an age coming for Derby.