But the hosts had to survive a late rally from Barnsley after substitute Jason Scotland brought them back into the game with a 72nd-minute header.
Nugent broke the deadlock in the 49th minute and then scored again in the 61st with his fifth penalty of the season as Leicester made it 13 points from five games at home.
Barnsley were dealt a blow when Peter Ramage, on loan from Crystal Palace, was injured in the warm up and had to be replaced by Tom Kennedy, a former Leicester player .
Goalkeeper Jack Butland, on loan from Stoke, and midfielder David Fox, on loan from Norwich, made their debuts for the Tykes.
Leicester manager Nigel Pearson named the same side that had won two and drawn one of the last three league games.
Pearson had warned that anyone who thought that it would be easy against Barnsley was a "fool," and the first half certainly proved the Tykes had no intention of letting Leicester overrun them.
They packed midfield and the home side struggled to find space until Nugent and Jamie Vardy got through but finished with weak shots.
Butland was called on to make his first save when Danny Drinkwater tested him with a long range shot in the 19th minute, but it was Barnsley who had the ball in the net two minutes later when Paddy McCourt set up Scott Wiseman only for the effort to be ruled offside.
McCourt was again the danger man in the 24th minute with a solo run and shot that brought a fine save from Kasper Schmeichel. That seemed to rouse Leicester and Butland tipped a fierce shot from Lloyd Dyer round the post and then saved Andy King's header.
Vardy brought the 20-year-old keeper to another diving save, but the best chance so far went to Dyer in the 38th minute.
Played in by Vardy he prodded the ball just wide with only Butland to beat.
The half ended with Anthony Knockaert flattened by a challenge from Yves M'Voto but referee Philip Gibbs waved aside penalty appeals.
After the frustrations of the first half, Leicester finally made the breakthrough in the 49th minute. Dyer found Nugent in space on the right-hand side of the penalty area and he drilled a low shot into the far corner of the net for his fifth goal of the season. His other four were all from the penalty spot.
And after Vardy and Drinkwater had come close to adding to the Foxes' lead, Nugent scored again in the 61st min - with another penalty. Vardy was brought down by Butland, who escaped with just a yellow card, and Nugent hammered the spot-kick into the top corner.
It was now all Leicester, but they were rocked in the 72nd minute with a goal against the run of play. David Perkins was allowed to cross from the left and poor defending enabled Scotland, a 64th-minute substitute, to place a simple header into the net.
It sparked a Barnsley fightback and Schmeichel had to pull off a stunning save to keep out a header from Martin Crainie in the 82nd minute, having tipped a shot from Tomasz Cywka round the post.
Vardy just failed to connect with a low ball in from Drinkwater in time added on and Leicester held out to preserve their unbeaten home record.