A first-half header from Moore and a late penalty by Nugent earned Leicester their victory over Wigan.
The win could have been even more comfortable had City taken all their chances in a match they dominated.
It was Leicester-born Moore's first goal for the club and Nugent's second of the season.
The victory was Leicester's fourth in the opening six games and cemented their place in the top four in the Sky Bet Championship.
Foxes manager Nigel Pearson, serving a one-match ban, was missing from the dugout, but he would have been delighted to see his decision to switch to a 4-4-2 formation pay early dividends.
There was far more pace and creativity about Leicester's play and Wigan struggled to keep them at bay.
Nugent fired just wide in the sixth minute and, in another sweeping attack, Jamie Vardy just failed to put Andy King clear with a neat pass on the edge of the penalty area.
Wigan's first attempt on goal came in the 10th minute, but Roger Espinoza's shot was deflected for a corner.
But Leicester's pressure saw them take the lead in the 15th minute. Wigan conceded a corner and then allowed 20-year-old Moore to come in unchallenged at the far post to bullet a header into the roof of the net from Anthony Knockeart's accurate cross. It was hometown boy Moore's first goal for City.
Wigan ventured forward very rarely but Ben Watson was only just off target with a 25-yard free-kick after a foul by Ritchie De Laet.
Knockaert and Nugent both missed good opportunities to add to Leicester's lead and, in the 42nd minute, Vardy broke at pace down the left and tested Scott Carson with a rasping shot.
But with the last kick of the half, Leon Barnett brought Kasper Schmeichel to his first save with a crisp shot on the turn.
Dyer's pace twice troubled Wigan in the opening minutes of the second half and it needed a great tackle by Espinoza on Vardy to prevent the City striker from converting a pass from Nugent.
Wigan boss Owen Coyle rang the changes bringing on three substitutes, including Manchester United loanee Nick Powell with an hour gone.
But Leicester should have scored a second goal in the 70th minute. Vardy showed good control inside the penalty area to set up Nugent, but his first-time volley flew well wide.
However, the same combination produced a goal in the 81st minute. Vardy was tripped by Beausejour and Nugent hammered home the penalty to clinch victory for Leicester.