Nugent struck after 65 minutes of Tuesday night's clash at Fratton Park, volleying home from 12 yards after latching on to Dave Kitson's flick on.
Pompey were on top for the majority of the match as Palace failed to really threaten as an attacking force.
The Eagles remain in relegation trouble, lying just three points clear of the drop zone having played two games more than third-bottom Scunthorpe.
Portsmouth made one change from the team that secured a narrow win against Barnsley on Saturday as Villa loanee Jonathan Hogg returned from suspension to take the place of the injured Liam Lawrence.
Steve Cotterill was only able to name five substitutes with Ibrahima Sonko not allowed to be on the bench as he would have been the sixth loan player in the squad.
There was also one alteration for Dougie Freedman's side from the weekend victory over Sheffield United as Sean Scannell came in for Wilfried Zaha.
Both sides could have taken the lead inside the first 15 minutes from corners.
First Pompey's Joel Ward volleyed wide from David Cotterill's delivery before Palace's on-loan Hull defender Anthony Gardner could only head off target from Darren Ambrose's set-piece.
After the even start it was the home side who began to get on top with Swansea loanee Cotterill giving Dean Moxey the run around down the Portsmouth right.
The Wales International put in a number of dangerous crosses and had a chance 21 minutes in after Nugent's shot was saved by Eagles goalkeeper Julian Speroni but he blazed wide from eight yards.
Pompey remained dominant for the remainder of the first period but they could not quite open up Palace, who remained resilient in defence without creating much in attack.
Portsmouth were again stronger at the start of the second half but only had Nugent's weak header over from Cotterill's free-kick after 54 minutes to show for their efforts.
The home side's pressure finally told after 65 minutes when Greg Halford's long throw was flicked on by Kitson and met on the volley by Nugent who mis-hit the ball but it bounced into the ground and over a helpless Speroni.
Palace should have been level just two minutes later when Ambrose found Patrick McCarthy in the box but he could only head wide from six yards.
Freedman tried to get his side back into the game with a double substitution on 73 minutes with Zaha and Jermaine Easter coming on for Neil Danns and Scannell.
But it did not make much of a difference as their only chance of an equaliser came when Zaha spooned wide from 12 yards four minutes from time as Pompey held out comfortably.