Steve McClaren's fourth-placed side came into the game having won eight of their previous 10 league games, but were comfortably beaten at the King Power Stadium on Friday.
A fine strike from Ritchie De Laet was all Leicester had to show for a dominant first-half display featuring 15 attempts at the Derby goal, but the visitors folded quickly after the interval despite an own goal from De Laet.
Leicester have now won five league games in a row and are firmly on course to seal a return to the top flight for the first time since 2004.
De Laet opened the scoring in the 25th minute, surging forward from the halfway line and exchanging passes with Nugent before finding the bottom-right corner of the net with a left-footed strike from the edge of the area.
Leicester hit the crossbar twice through Jamie Vardy and Liam Moore, but their lead was doubled three minutes after the break when a shot from Nugent bounced back off Jake Buxton only to hit the striker again and ricochet into the net.
Derby were handed a route back into the game in the 59th minute when De Laet inadvertently diverted a header from Buxton beyond his own goalkeeper, Kasper Schmeichel.
However, Nugent restored his side's two-goal cushion almost immediately with a penalty after Craig Forsyth had needlessly brought down Vardy.
The hard-working Vardy then added a fourth after 64 minutes, finishing coolly following a neat throughball from Nugent.
