Hughton was sacked on Thursday morning with Forest rooted to the foot of the Championship table and while they remain bottom, they managed to claim a morale-boosting victory at the John Smith's Stadium under interim head coach Steven Reid.
A first-half strike from Lewis Grabban and an own goal by Lee Nicholls just after half-time saw Forest not only pick up their first Championship win after six defeats in seven matches, but it is also the first time they have scored more than one goal in a league game since April.
Huddersfield, meanwhile, have now lost two of their last three league fixtures following a positive start to the campaign.
Forest were rewarded for their bright start to the match as Grabban put them ahead in the 22nd minute. Brennan Johnson picked up the ball inside his own half and used his blistering pace to beat Levi Colwill before putting in a fine cross to meet the diving head of Grabban, who steered the ball inside Nicholls' front post.
There could be an argument that Grabban should have had two goals in the first 20 minutes as he also struck a volley straight at Nicholls. Manchester United loanee James Garner played in a beautiful ball to find an unmarked Grabban who should have done better.
After downing Blackpool 3-0 in midweek, Huddersfield looked disjointed in their build-up play and rarely strung multiple passes together. Town began to keep more possession after falling behind but threatened very little when going forward and the visitors were organised at the back and at half-time were by far the better side.
Forest continued their fine start to the match with an even better start in the second half as just three minutes after the restart, they doubled their lead through a Nicholls own goal.
Ryan Yates' effort from distance was mishandled by Nicholls who parried the ball into the feet of Joe Lolley. Lolley's strike from the six-yard box took a deflection off Nicholls and into the back of the net. Nicholls could only blame himself for not holding onto Yates' effort from distance which presented a wonderful opportunity for Lolley to strike.
Huddersfield's reaction to going two goals behind was similar to the way they responded to conceding the first. Carlos Corberan's side yet again started to get a hold of possession but remained lifeless in front of goal and never troubled Brice Samba.
Coberan's frustration started to show in the final few minutes as his side allowed the match to peter out without ever putting up much of a fight.