Ferriby got their goal 11 minutes from time when Paul Musselwhite came out to punch a corner but missed. Nathan Stead placed the ball into the goal, and the linesman adjudged Mike Price's headed clearance to be from behind the line, so the goal stood.
Ex-Tiger Rob Dewhurst lifted the trophy as Ferriby's captain.
City line-up (4-3-3): Musselwhite; Petty, Whittle, Mohan, Holt; Greaves (Mann), Philpott, Peat; Itonga (Bloomer), Donaldson (Bradshaw), Price.