Nugent, who scored his 100th career league goal in the 2-1 win over Burnley on Wednesday, ending an 11-game drought, put the hosts ahead after seven minutes and was on hand to restore their advantage after Jay Simpson's leveller.
He waited until stoppage time to complete his treble as the Foxes climbed eight places to seventh and Nigel Pearson claimed the bragging rights over his old employers.
The defeat denied the Tigers, who had lost only one of their opening six games, the opportunity to go joint top of the table.
Nugent's early opener arrived when he intercepted Danny Drinkwater's attempt at goal and took advantage of the wrong-footed Ben Amos to steer home.
The Foxes almost doubled their lead immediately as Jamie Vardy showed his strength to hold off two defenders before unleashing a shot which was deflected just wide.
And from the resulting corner there was uncertainty in the Tigers' box as Wes Morgan headed on for Vardy, whose goal-bound strike hit team-mate Sean St Ledger before being scrambled clear.
With the visitors rocking amid a downpour in the east midlands, a brief glimpse of an opportunity momentarily raised their hopes only for the offside flag to thwart Simpson as he looked to latch onto Robert Koren's neat pass.
But moments later they were level. Corry Evans picked out Sone Aluko and his cross-cum-shot from the right side of the box was turned in by the ever-alert Simpson.
Leicester mounted a spirited response to the setback as Drinkwater received Anthony Knockaert's pass before skipping past Evans and drilling a powerful effort narrowly over.
Nugent doubled his tally and restored the home side's lead three minutes before half-time. Knockaert kept the ball alive after Ahmed Elmohamady cleared Ben Marshall's effort on the line, the French winger delivering a cross for Nugent to head in from close range.
Pearson's side raced out of the blocks after the interval and should have made it 3-1 when Vardy was put in the clear by Knockaert, but the former Fleetwood striker put his shot too close to Amos and it was clipped behind for a corner.
It served as a wake-up call for Steve Bruce's charges, who soon called Kasper Schmeichel into action as Aluko's 25-yard thunderbolt had the Dane scrambling across goal to tip wide.
The Tigers boss introduced Nick Proschwitz from the bench for the final 12 minutes, hoping to see the £2.6million German striker open his account for the club, but it was the hosts who threatened next.
Alex Bruce handled the ball on the edge of the box and, despite Nugent's appeals for a penalty, a free-kick was given and Knockaert's effort was plucked out of the air by Amos.
Steve Bruce was sent to the stands in the closing stages - punishment for his reaction to a questionable call from the linesman, who adjudged the ball to have crossed the sideline as Hull tried to break clear.
Pearson had cause for complaint next when six minutes was added on and Hull almost grabbed a dramatic leveller. Elmohamady's header from a corner was destined for the back of the net, only for Knockaert to clear off the line.
But Martyn Waghorn picked up the loose ball, found fellow substitute Lloyd Dyer and he picked out Nugent, who slotted past Amos to seal the win.
