Charlton established a new post-war club record of 10 consecutive top-flight London derbies undefeated as two St Stephen's Day bloopers ensured a blank scoreline at chilly Craven Cottage.
Jason Euell's error came when he tackled Andy Melville but hit the post when one-on-one with the Fulham goalkeeper Edwin van der Sar - and then home striker Louis Saha was guilty of a miskick when in a great shooting position.
The first half was a disjointed affair, with neither side discovering the fluent passing football which they are capable of.
After the break, van der Sar almost scored a disastrous own-goal before making a world-class double-save to keep the scoreline blank.
A late flurry of chances also failed to break the deadlock.
Charlton boss Alan Curbishley dropped Portuguese international Jorge Costa, who started as centre-back in Saturday's 2-0 defeat by Blackburn. He was on the bench alongside John Robinson - who returned after missing two matches with a groin injury.
Home manager Jean Tigana also revamped his starting line-up, dropping John Collins and Luis Boa Morte, who both played in the 4-0 thrashing at Tottenham 11 days ago.
FULHAM: Van der Sar, Finnan, Melville, Goma, Brevett, Legwinski (Collins 63), Malbranque, Davis, Clark (Boa Morte 12), Saha, Hayles. Subs Not Used: Taylor, Ouaddou, Stolcers. Booked: Boa Morte, Hayles.
CHARLTON: Kiely, Fortune, Fish (Costa 45), Konchesky (Robinson 74), Young, Parker (Bart-Williams 79), Stuart, Jensen, Powell, Lisbie, Euell. Subs Not Used: Johansson, Roberts.Booked: Parker.
Referee: S Bennett (Kent).