Simon Russell won an 88th minute penalty which he took himself and scored, and Russell Fry wrapped it up with a third goal.
Skipper Michael Byron lifted the trophy in front of an 876-strong crowd.
City line-up: Harvey, Matthews, Cattermole, Tomlinson, Wiseman, Byron, O'Neil (Beattie 73), Cooper (Ashley Allanson 73), Hotte (Benson 68), Fry, Russell.
Un-used subs: McGary, Arron Allanson.