Wednesday, who had not won any of their last seven games in all competitions, started brightly and saw Royston Drenthe's effort from the edge of the box fly narrowly wide on 13 minutes.
The Dutch midfielder, who is on loan from Reading, then put his side ahead with a long range strike on 27 minutes.
Rhoys Wiggins went close to restoring parity when his shot came within inches of the post on 69 minutes.
However, seconds later, Wiggins beat two Wednesday defenders and found Igor Vetokele in the box, who applied the finish for his seventh goal of the season.
Charlton then survived shouts for a penalty from the away side after Atdhe Nuhiu appeared to be fouled in the box.
Vetokele nearly snatched all three points for the home side when Jordan Cousins found the striker after a quick Charlton break, but he fired narrowly wide.