Luke Chambers made the breakthrough with less than 20 minutes remaining before Forest made the game safe with a second goal, credited to Dexter Blackstock.
Another win and another clean sheet to add to Sunday's success at Plymouth means Billy Davies' side are now 14th in the Championship with 13 points from 10 games.
Saturday's trip to Peterborough completes a sequence of three games in six days for the Reds, who could move into the top-half of the Championship ahead of the international break if they make it nine points out of nine.