Fulham had lead through winger Damien Duff but the Addicks hit back, with goals from Johnnie Jackson and Yann Kermorgant.
Duff combined with Alex Kacaniklic and the young Swede teed up the Irishman to open the scoring with a neat sidefoot from seven yards out.
After the break, Jackson found the unmarked Bradley Pritchard but his shot was brilliantly saved by Mark Schwarzer.
Duff then went close to nabbing a second but his effort was deflected against his own bar by Palace defender Chris Solly.
The Championship side grabbed the equaliser on 70 when Jackson beat the offside trap and slotted the ball past Schwarzer.
The Addicks sealed the win just seven minutes later when Kermorgant lashed home a half-volley from the edge of the box.