Sean Scanell scored the only goal of the game just before half-time to make the Terriers mathematically safe from relegation.
For Nottingham Forest, in front of 21,572, it was another disappointing afternoon as their season slowly fades away.
The Reds remain 9th in the table but can now go no higher. They entertain promotion-chasing Watford at the City Ground on Wednesday night in their penultimate home fixture.
Speaking to the official NFFC website after the game, Dougie Freedman said: “We were disappointing in the first 25 minutes. We didn’t show enough energy.
“I feel that, since I’ve been at the football club, the huge output of energy that was required to lift us away from the bottom of the table is now catching up with us. That showed today. I think players are breaking down through injury and we’re just running out of steam a little bit."