The home side should have been out of sight in the first 25 minutes as they scored, twice hit the woodwork, and spurned other chances before two fine individual goals and some poor defending allowed the Yorkshire side to take a 2-1 interval lead.
Despite constant pressure in the second half Charlton failed to break down the Owls 4-5-1 formation and were booed off the field at the end by the frustrated supporters.
Charlton could have taken the lead after seven minutes when on-loan defender Linvoy Primus, making his second debut for the Londoners, 15 years after he first played for them headed the ball against the post.
Charlton took the lead on 18 minutes when Nicky Bailey's free-kick was headed into the path of Luke Varney by Andy Gray and Varney poked the ball into the net.
The Charlton striker then hit the post and Gray blasted the rebound over from close range.
Wednesday took a shock lead on 38 minutes when Wade Small went on a mazy run through the Charlton defence before firing home an angled shot which went in off the post.
Three minutes later the Charlton defence back-pedalled as Marcus Tudgay broke into the penalty area and he was unchallenged as he fired low into the net.
Despite bringing on three substitutes during the second half, Charlton were unable to get an equaliser despite battering the visitor's defence with Wednesday goalkeeper Lee Grant making a couple of fine saves to keep his side ahead in the game.