Fulham, who made themselves safe with a win against Everton last week have taken ten points from their final five games and this victory was their third over Charlton this season, having also beaten them in the FA Cup.
After securing their Premiership future a few weeks ago, Charlton's season has disintegrated with only one win in their seven Premiership matches and it is 16 years since they last won their last League game of any season.
They were the better side in the first half and the penalty came after 31 minutes when Charlton Dean Kiely brought down Saha in the area and was sent off by referee Dermot Gallagher.
Reserve keeper Ben Roberts went in goal, but could not save Saha's spot-kick.
In a rare first-half attack, Jason Euell screwed a shot across the face of the goal.
After the break ten-man Charlton battled well for an equaliser and Fulham keeper Maik Taylor made two great saves to deny Kevin Lisbie.
Charlton had the chance to level when Euell was brought down by Alain Goma, but the striker's penalty was turned away for a corner by Taylor.
The home side knew it wasn't going to be their day when other chances went begging and Fulham held on for the win to end their season in impressive style.