The promotion-chasing Rams had to hold on for a point in the end, as the Cottagers were again left frustrated on home soil in a match that they will argue they should have won.
Fulham are now unbeaten in eight matches here against Derby, with six of those finishing all square, but their failure to pick up all three points means that they are stuck down in 17th place.
Fulham were just about the side on top in the opening quarter of the match, but that Ayite header was the closest either team came to scoring prior to Norwood's breakthrough strike on the half-hour mark.
The Brighton & Hove Albion loanee lofted a free kick over the wall and past the reach of Carson, who appeared to be a little unsighted as the ball floated past him.
Not a great deal separated the sides in a first half of few chances, and Derby will therefore feel that they merited their goal when it arrived through a fine Vydra finish shortly after the restart.
David Button was needed to deny David Nugent from a promising position soon after, as County looked for a quick-fire second, while up the other end of the field Luca de la Torre should have done better with his headed chance.
Derby had to dig deep at the end with some frantic defending, seeing the job through to put their disappointing 4-2 loss against Reading last time out behind them.