The result condemns the relegated side to their fourth defeat in the Championship in four games.
Christie might have put his side in front 10 minutes later had he not struck his shot straight at the keeper from the centre of the Fulham box.
In a half predominantly dominated by the hosts, Derby took the lead in the 23rd minute when Ward finished neatly into the top corner having been found by Russell's cross.
Fulham failed to create much of real note, but Konstantinos Stafylidis might have done a little better from the edge of the box as he slashed wide of goal despite having time on the ball.
Parity was not to last too long, though, with Derby's Russell providing again. This time it was Bryson who converted low down past Jesse Joronen in the 59th minute.
County secured the three points just minutes later when Christie fed in Martin, who finished neatly with his left to make it 3-1, before the striker bagged a brace to move the hosts further ahead.
Fulham's Championship humiliation was summed up when substitute Simon Dawkins converted from the left side of the box, 10 seconds after the restart, to leave the final score at 5-1.