The Final against Doncaster Rovers was delayed until this evening due to their involvement in the play-offs - which they won - last season.
After a goal-less 90 minutes, the game went to extra time. A further half an hour passed without either side breaking the deadlock, before City midfielder Ed O'Neil grabbed the winner in stoppage time.
The double-winners kick off the new season on Wednesday 20th at Huddersfield.
City line-up (4-4-2): Musselwhite; Regan, Burton, Holt, Smith; Russell, Melton, Fry (O'Neil 45), Peat; Donaldson, Webb (Benson 90).
Un-used subs: Harvey, Cooper, Wiseman.