Early goals from Scott Parker and Hugo Rodallega put the Whites in control and they saw out a difficult second-half period unscathed before the Colombian added a late third to earn caretaker boss Kit Symons another win.
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Parker gave the hosts the lead on six minutes against the club with whom he started his career.
The former England midfielder smartly stole the ball in the Charlton half and drove to the edge of the box before slipping in Ross McCormack, whose return pass allowed Parker to thrash home via the crossbar.
Fulham were two up six minutes later, with McCormack again involved. The £11m striker's instinctive chest control set himself up for a volley which was parried by Stephen Henderson, and Rodallega had the simplest of close-range conversions.
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Tim Hoogland should have headed them further ahead when he glanced a McCormack free kick just wide from six yards, while Rodallega fired powerfully over after spinning away from his marker.
Charlton, who could have gone third in the table with a win, started the second half as quickly as Fulham did the first, but could not get on the scoresheet as Bikey shot at Marcus Bettinelli and Tucudean struck wide.
Fulham thought that they had a third when Hoogland bundled over the line following a Dan Burn flick on, only for the offside flag to deny him, and should have been out of sight when Bryan Ruiz sliced over McCormack's cross.
Henderson kept his misfiring teammates in the contest with good saves from Rodallega and Cauley Woodrow late on, but could do nothing to prevent the former securing the points in the 87th minute.
Lasse Vigen Christensen saw the overlapping run of Rodallega and timed his pass perfectly for the striker to cut inside Tal Ben Haim and guide a left-footed shot into the bottom corner, as Symons strengthened his claim for the permanent job with a fifth win in eight games.
The result takes Fulham to 19th, while Charlton remain seventh after a second loss of the season.