An uninspiring game failed to produce any goals, but Charlton will be disappointed not to have left with all three points.
Shaun Bartlett missed two great first-half chances, before Paul Konchesky had a great strike acrobatically saved by Van der Sar late on to deny the Addicks a win that would have helped their UEFA Cup push.
Fulham almost fell behind straight away as Bartlett was guilty of missing a sitter. Good build-up play between Konchesky and Danny Murphy ended with Bartlett arriving unmarked at the far post.
It seemed simple to just prod the ball into an empty net, only for the Addicks striker to tread on the ball before Alain Goma cleared the danger.
Zat Knight came within inches of breaking the deadlock on 19 minutes as former Charlton midfielder Claus Jensen caused chaos with a corner kick.
The Fulham defender rose at the far post but his effort drifted inches wide.
Minutes later it was again Knight who went close to breaking the deadlock, this time with a thundering 30-yard drive.
Dean Kiely fumbled his strike but no Fulham player followed up, and Charlton quickly broke away. Luke Young beat Carlos Bocanegra down the right flank and sent in a low cross.
Matt Holland managed to get a touch on the ball before Bartlett hit a shot on the turn and Van der Sar got down quickly to block with his feet.
Steed Malbranque started for the first time since January after overcoming an ankle injury, and he desperately tried to force a breakthrough.
The Frenchman teased the Charlton defence before teeing up a cross for Alain Goma, but he was unable to hit the target with a tricky header.
On 27 minutes Danny Murphy cut inside before sending a weak shot wide and moments later he forced Van der Sar to make a full-stretch save with a rasping 25-yard drive.
Fulham created the first chance of the second half when Jensen dinked in a cross which Goma diverted towards goal, but Kiely got down well to save.
Radostin Kishishev and then Liam Rosenior tried long-range efforts for each side as play continued to sweep from end-to-end, and with 15 minutes left the home side were left thanking their goalkeeper.
Van der Sar produced a fantastic one-handed save as Konchesky's strike from the edge of the box seemed destined for the top corner.
Coleman and his side left the field to a chorus of boos while Charlton will be buoyed by a vital away point.
MAN OF THE MATCH: Edwin van der Sar (Fulham) - Made several crucial saves throughout the match, none more important than the last-minute stop that denied Konchesky.