Luis Boa Morte's superb double strike sandwiched Charlton's only goal through Jason Euell. Alan Curbishley will now have to hope the Addicks' season does not peter out completely following their FA Cup exit to Middlesbrough on Wednesday.
Charlton started the better and had a great chance to take the lead after nine minutes. Matt Holland's ball over the top sent Darren Bent racing away but the England hopeful's first touch let him down.
Yet instead it was Fulham that went ahead after 15 minutes with a goal that Thomas Myhre will want to forget.
The home side won a free-kick on the right-hand edge of the penalty area after Gonzalo Sorondo had brought down Heidar Helguson. Simon Elliott stood over the ball but it was his captain Boa Morte who whipped a low ball past Charlton's two-man wall and inside Myhre's unguarded near post.
The advantage could have been cancelled out by Jason Euell three minutes later but he tamely headed Darren Ambrose's cross straight at Antti Niemi from barely five yards out.
However, the ex-Wimbledon star made amends on 25 minutes. Ambrose's left-wing corner was feebly punched by Niemi and Hermann Hreidarsson hooked the ball back towards goal. It looked like it was heading in but Euell made sure as he headed the ball over the line from three yards out.
One minute later and there was more chaos in the Charlton defence when Liam Rosenior and Zat Knight allowed Darren Bent to get a shot away from just inside the penalty area which Niemi did superbly to turn around the post. The two Fulham defenders blamed each other for the mix-up and had to be forcibly separated by their team-mates.
Daren Bent's miss became all the more glaring when Boa Morte restored Fulham's lead on the half-hour. If his first strike was opportunistic, the second was world class. The Portuguese winger picked the ball up 50 yards out and ran straight at the heart of the creaking Charlton defence.
Sorondo tried to keep up but was brushed aside and, from just inside the area, Boa Morte slotted the ball past the despairing Myhre.
Fulham were content to sit back and defend their lead in the second half and, although Charlton dominated possession, they failed to seriously test Niemi until the game's closing stages.
The better chances actually fell to the home team. On 66 minutes Boa Morte came within a whisker of grabbing a hat-trick when his deflected free-kick was cleared off the line by Euell.
Right at the death Charlton had two chances to rescue a point. First Marcus Bent saw his fierce shot from just inside the area tipped over by Neimi. The Finnish shot-stopper then did even better to keep out Hreidarsson's powerful header with his feet, but it was a case of too little too late for Charlton.