Adlene Guedioura was close to opening the scoring for Forest early on but the midfielder's strike rebounded off the crossbar, with the Charlton defence breathing a sigh of relief.
The hosts continued to dominate possession and broke the deadlock in the 17th minute when McGugan curled in a free kick that flew past Ben Hamer in the Charlton goal.
Chris Powell's side struggled to create chances but could have converted a surprise equaliser through Johnnie Jackson, but the midfielder's header went wide of the post.
Charlton's defence improved in the second period and Forest were reduced to long-range efforts, with Andy Reid going close with a volley for the home side.
Guedioura could have extended the lead but his deflected effort sailed agonisingly over the bar.
The visitors started to enjoy more possession late in the game but Hamer was forced into action to block a Simon Cox shot as Forest searched for a goal to wrap up the match.
Hutchinson did manage to find a goal with 15 minutes remaining as the youngster provided support following a set piece before collecting the ball and slotting past Hamer.
The Hutchinson strike proved to be the winner after Fuller came off the bench to score a late goal for Charlton but Forest survived the late pressure to hold on for the victory.