It was the home side that started the better and they had a penalty shout turned down after seven minutes when Jake Buxton appeared to handle inside the area, but no decision was forthcoming.
Derby had a half-chance to take the lead after 12 minutes when Connor Sammon advanced into the Forest box, but his effort was always rising over the crossbar.
Meanwhile, the match started to become scrappy as the half advanced with a host of dangerous challenges raising the temperature.
Chances remained few and far between in the latter stages of the half as the two sides entered the break level.
The match remained cagey in the early stages, but Derby took the lead after 54 minutes when Bryson tapped home at the far post to score his second league goal of the season.
Forest had a half-chance to level the score just before the hour mark when Simon Cox pounced in the box, but his effort was wide of the target.
The home side continued to push in the latter stages, but they never really threatened as Derby held on for a vital three points.