Nigel Pearson's Foxes restored their seven-point lead over second-placed Burnley and now need just three more points from their last three games to go into the Premier League as champions.
Nugent scored the only goal of the game with a superb finish from a narrow angle in the 67th minute, and 11 minutes later the visitors
- still waiting to guarantee their play-off place - had Benoit Assou-Ekotto sent off for a second bookable offence.
Nottingham Forest nudged back into play-off contention as they ended their dismal run of 12 league games without a win with a tight 1-0 triumph over relegation-threatened Birmingham at the City Ground.
Matt Derbyshire struck the only goal of the game in the second minute to move Forest within three points of sixth-placed Brighton - whom they will face on the final day of the season.
But Mick McCarthy's Ipswich blew their chance to move into the top six as their run of two straight victories ended in a 3-1 defeat to Watford at Vicarage Road.
Albert Rieira struck the opener for the home side after 21 minutes and although Anthony Wordsworth equalised five minutes after the break it was Watford who always looked more likely to take the points.
Gabriele Angella headed home a free-kick in the 63rd minute to put the home side back in front and Lewis McGugan sealed the points two minutes later.
Stefan Maierhofer scored twice as Millwall surged out of the relegation zone with a potentially crucial 2-1 win at Middlesbrough.
The Austrian defender, who had never previously found the net for the Lions, gave the visitors a dream start when he turned in Lee Martin's cross on 16 minutes.
And Maierhofer produced a near-carbon copy from another Martin cross on the half-hour to double Millwall's lead, before Emmanuel Ledesma's effort 10 minutes from time led to some anxious late moments.
The win - Millwall's third in a row away from home - lifted Ian Holloway's side above Charlton and Blackpool with three games of the season still to play.
But there was gloom for fellow strugglers Barnsley who remain rooted in the bottom three after a 1-0 home defeat to Yorkshire rivals Leeds.
Ross McCormack's 29th goal of the season in the 16th minute proved enough to earn a second straight win for Brian McDermott's men and leave the sinking Tykes three points off safety.