There were three divisions and 65 league places between the sides at the start of play, but the hosts were lethargic for long spells and County should have taken advantage.
But the difference between the teams was in the quality of finishing, with Davies and Zamora firing home in the first half before Duff and Okaka added some late gloss to the scoreline.
And the result means that County will be able to concentrate on their promotion bid from League Two, as well as sorting out their off-field situation, which was thrown into further doubt earlier in the week when the club was sold to Ray Trew for just £1, leading to the exit of director of football Sven-Goran Eriksson.
The Swede was lauded by County's fans, but the grand plan he signed up to when the club were bought by Munto Finance last summer has been a failure, although they were far from outclassed here.
Indeed, they could have taken a shock lead when Ben Davies forced Mark Schwarzer to use all of his 6'4" frame to tip over his 25-yard drive.
Yet County were undone by another Davies, in this case Fulham winger Simon. The Welshman has had a torrid time recently with a niggling foot injury, but took his goal superbly.
It appeared the chance had gone when Danny Murphy's ball over the top forced him away from goal, but Davies simply used County skipper John Thompson as a shield, firing through the defender's legs and into the far corner of the net for his first goal in 11 months.
But County would have been level just before half-time were it not for a superb save by Schwarzer. Craig Westcarr did superbly to fox Chris Baird before driving low across goal, only to be denied by the Australian's fingertips.
You had the feeling County would regret not taking their chances, and so it proved as Fulham doubled their lead two minutes later.
It was not a goal that the visitors will remember fondly as David Elm was allowed to flick the ball to his strike partner, who outmuscled Stephen Hunt before volleying past the exposed Kasper Schmeichel.
It appeared to be game over but, to their credit, County kept attacking in the second half and Ben Davies twice had Schwarzer scrambling across his goal with efforts from distance.
Yet although County were giving as good as they got, you always had the feeling Fulham could step up a gear if required, and so it proved when Duff latched on to Zamora's throughball, cut inside and flashed a shot inside Schmeichel's near post.
If that was cruel on County then it got even worse with 11 minutes to go. The visitors defence went absent without leave allowing Okaka to run on to Nicky Shorey's pass and smash the ball through Schmeichel's legs to record his first goal for the club.