His first came four minutes before half time, finishing Jamie Forrester's left-wing cross at the far post.
It was another left wing cross that provided his second. This time Andy Holt claimed the assist for Fearns's 79th minute header.
Chris Greenacre pulled back a consolation goal for Stoke 5 minutes from time, but the 2-1 scoreline marked City's third successive victory in the Pontins League.
Chris Brass, Dave Penney and Nigel Clough - managers of York, Doncaster and Burton Albion respectively - were reportedly among the 171 crowd.
City line-up (4-4-2): Musselwhite; Wiseman, Whittle, Strong, Burton; Regan, Melton, Russell, Holt; Fearns, Forrester.
Un-used subs: Harvey, Benson, Byron, Cooper, Tomlinson.