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.
The Reds 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.
Barnsley manager Flitcroft praised the “fighting spirit of his players “ and felt they deserved better than finding themselves bottom of the table.
Flitcroft said: “I am not naive enough to think I am not under pressure but I am up for the fight. And so is this group of players. I have seen the first goal from Scott Wiseman that was disallowed and it was about half a yard onside.”