Ross McCormack’s 14th goal of the season put the Whites ahead before Johann Gudmundsson equalised for the hosts.
It means Fulham are now eight points clear of third-bottom Millwall with five games left as they continue to limp towards the end of a season everyone at the club would probably rather forget.
Having given every other team in the division a head start by failing to win any of their first eight matches under the hapless Felix Magath, their revival under Kit Symons was short-lived but will surely be enough to ensure they avoid back-to-back relegations.
They took the lead with a well-worked goal after just eight minutes, when centre-half Michael Turner lofted the ball to the edge of the penalty area. Matt Smith’s improvised back-header looped over his marker and sat up perfectly for strike partner McCormack to nod over Addicks keeper Stephen Henderson and into an empty net.
Charlton have little to play for in mid-table so their fans took a break from booing Scott Parker – he left more than 11 years ago but time is clearly not a great healer in this part of south London – to greet the goal with a burst of ‘Millwall are going down’.
The lead lasted just 10 minutes, however, before Morgan Fox whipped in a low cross and Gudmundsson arrived at the far post to smash the ball into the roof of the net. Fulham keeper Marcus Bettinelli seemed convinced the Icelander was offside and made his opinion clear to the assistant referee, but to no avail.
Fulham were carved open again just before the half-hour mark and only Gudmundsson will know how he did not fire Charlton into the lead. When Igor Vetokele’s cross reached the midfielder he was five yards out with half an empty goal to aim at, but he somehow planted his shot into the side netting.
Fulham, knowing a victory would lift them to the heady heights of 18th, searched for a winner with Smith firing just wide from the edge of the area before seeing a header cleared off the line by Joe Gomez.
Charlton threatened late in the second half with Tony Watt firing wide and Bettinelli denying Chris Eagles. But it was Smith who missed a golden opportunity to win it for Fulham when he blazed over in the last minute to ensure the agony will be prolonged for a little longer yet.