Goals from Jean-Yves M'voto and Tom Kennedy did the damage at The Valley, as Jose Riga's side fell to a fifth defeat under the Belgian.
M'voto opened the scoring with a thumping header, scoring his first goal for the club in the process.
Kennedy's effort had a touch of fortune about it as a mis-hit cross floated over home goalkeeper Ben Hamer and in.
Astrit Ajdarevic grabbed a late consolation, but it was not enough for Charlton, who remain just a point above the drop zone, and two clear of Barnsley in 23rd.
Elsewhere, Luton Town's return to the Football League was confirmed as Cambridge United fell to a 2-0 defeat at Kidderminster Harriers.
Richard Money's side led the way in the Conference for much of the season, but a collapse allowed Luton to charge ahead with a 27-game unbeaten run playing a huge part in their promotion.
In League One, Crawley Town all but secured their safety with a comfortable 2-0 win at home to Tranmere Rovers.
Matt Tubbs' free-kick and substitute Gwion Edwards' effort with his first touch of the match sealed the points for John Gregory's side.
Tranmere had won their first game after Ronnie Moore's sacking as manager at the weekend, but defeat leaves them looking over the shoulder, just three points above the bottom four.
