However, the Addicks had goalkeeper Dillon Phillips to thank for helping them get a point as he made some brilliant saves in the match.
Earlier, Conor Gallagher put the visitors 1-0 up at half-time but Ivan Cavaleiro’s long-range effort just after the break levelled the scores.
Macauley Bonne’s header restored Charlton’s advantage but Aleksandar Mitrovic’s scrappy finish ensured both sides shard the spoils.
Fulham were the more likely side at the end but were nowhere near at it in the first half and Lee Bowyer’s side had a deserved lead at half-time.
In a rare moment of quality in the first-half, Chelsea loanee Gallagher’s sweeping finish rounded off an effective counter-attack.
Gallagher played the ball out left to Jake Forster-Caskey after good hold up play and the midfielders brilliant cross-field ball found Chris Solly who headed the ball down to Gallagher, who did the rest.
The hosts were a different team after the break with substitutes Bobby Reid and Harrison Reed giving them some much-needed flair going forward.
And on 55 minutes, Fulham got their equaliser when Cavaleiro broke into space on the right and his rasping effort flew into the roof of the net.
But Charlton re-took the lead two minutes later when Bonne flicked in Darren Pratley’s searching cross from the left following a goalmouth scramble.
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