Dodd struck in the first half and Trafford gave Tony Hesketh's men a two goal advantage in the second period.
Slyne pulled one back late on to set up a nervy finish.
But Fulwood kept them at bay to seal the trophy.
They are still on for a league and cup double if they can haul in Thornton Cleveleys at the top of the West Lancashire League Premier Division with six games to go.
Click here to see Steve Taylor's excellent photos from last night.
Keep up-to-date with our exclusive email newsletters.
Subscribe