Dennis Rommedahl scored twice as Charlton survived an FA Cup scare.
He put Charlton ahead from close range after 13 minutes but Paul Heckingbottom headed an equaliser four minutes later.
Matt Holland's calm finish restored Charlton's lead 10 minutes later, and Rommedahl added a third just before the interval from Darren Bent's cross.
Heckingbottom gave Wednesday hope with another header after 61 minutes, but Bent raced clear to seal Charlton's win with three minutes left.
It ended a run of four consecutive away defeats for Alan Curbishley's side and ended a sequence of eight losses in 10 matches.
Having lost to Championship opposition in the previous two seasons, victory will have come as a welcome relief for the Addicks.
For Wednesday, struggling in the Championship, a battling performance will boost boss Paul Sturrock.
Sheff Wed: Lucas, Heckingbottom, Coughlan, Simek, Wood, Whelan, O'Brien, Brunt, Partridge (Bullen 76), Corr, Tudgay.
Subs Not Used: Adamson, Diallo, Rocastle, Thorpe.
Goals: Heckingbottom 16, 61.
Charlton: Myhre, Hreidarsson, Powell (Perry 81), Spector, Fortune, Kishishev, Holland, Rommedahl (Ambrose 45), Hughes (Lisbie 77), Bent, Bartlett.
Subs Not Used: Andersen, Young.
Goals: Rommedahl 13, Holland 27, Rommedahl 44, Bent 87.
Ref: P Dowd (Staffordshire).