Lewis McGugan scored for the second league game running to give Forest a 17th-minute lead and on-loan Chelsea defender Sam Hutchinson netted his first senior goal after 75 minutes.
An own goal by Reds goalkeeper Lee Camp two minutes from time set up a nervy finale for the hosts but they saw out the remaining time to seal a deserved win.
Forest totally dominated the first half, with McGugan pulling the strings in midfield.
Charlton arrived at the City Ground also unbeaten since their promotion back to the second tier but the Addicks never looked like returning to south London with that record intact, rarely worrying Camp in the Forest goal until it was too late.
Hutchinson, McGugan, Adlene Guedioura and Dexter Blackstock came back into the Forest team after O'Driscoll had given some of his fringe players a run out against Wigan in the Capital One Cup in midweek.
Deadline-day signings Billy Sharp and James Coppinger were included on the bench.
Charlton boss Chris Powell just made one change with Jordan Cook replacing the absent Dale Stephens.
Powell brought in David Button on a two-year deal from Tottenham this week and the keeper was amongst the substitutes as cover for Ben Hamer.
Forest started brightly and almost went ahead after eight minutes but Guedioura's shot from inside the area hit the crossbar.
O'Driscoll's side went ahead shortly afterwards. McGugan was credited with the goal when his free-kick from wide on the left touchline was missed by Hamer and sneaked inside the post without a touch from anyone inside the crowded penalty box.
It might have been 2-0 straight away had Blackstock done better with his header from 12 yards out.
Simon Cox brought a solid save from Hamer just before half-time as Forest went into the break only one goal ahead, but leading comfortably.
Camp was called into action early in the second half to keep out an effort from Cook, which he needed two attempts at grasping.
Hutchinson gave Forest a two-goal cushion with a neat finish following Blackstock's lay-off and it appeared to be game over, with O'Driscoll bringing on new recruits Sharp and Coppinger for late run outs.
However, recent Charlton signing Ricardo Fuller played a part in the visitors getting a goal back.
The debutant's close-range header struck a post but somehow found its way into the back of the net via Camp's head from the rebound.
Forest held on, despite the late setback, and moved up to third in the table.