Charlton's second-half hero was their giant striker Chris Iwelumo - signed in the summer from Colchester United - who scored two of the goals with the other one coming from skipper Andy Reid.
It was a shattering result for Wednesday, who raced into a two-goal lead after only 15 minutes with Charlton defending poorly and unable to make any impression, although they had the first chance of the game when Jerome Thomas shot just wide.
It was the visitors who took the lead when Charlton failed to clear a corner and Burton O'Brien scored with a well-struck effort.
There was worse to follow for the home side as Tommy Spurr was left unmarked from another corner to head past Nicky Weaver.
The home side, who had to replace defender Ben Thatcher just before the break, were booed off at half-time.
However, an interval rocket from manager Alan Pardew transformed the home side as they took complete charge of the game and pulled a goal back after 51 minutes when Reid scored with a right-foot volley after good work from Darren Ambrose.
There was one scare for the Addicks as Richard Wood's header was scrambled away, but Charlton generally laid siege to the visiting goal and got the equaliser on 67 minutes.
China international Zheng Zhi, who had come on as a substitute, threaded the ball through the Wednesday defence and Iwelumo, holding off a challenge, took his goal well to level the scores.
The South Yorkshire side were now under severe pressure and barely got out of their own half and goalkeeper Lee Grant did well to tip over Reid's free-kick.
But with time running out, Iwelumo scored his second goal of the game after beating two men with his strength before slotting the ball past the visiting goalkeeper to settle an entertaining match.