Wales international Wes Burns gave them a first-half lead, which was doubled by Omari Hutchinson early in the second with a shot from the edge of the box.
The Blues host Huddersfield Town live on Sky Sports in their biggest match for 22 years on Saturday, knowing a point will take them back to the Premier League (KO 12.30pm).
A host of Town legends are set to gather for a black-tie gala evening celebrating the life of Kevin Beattie on Friday 17th May raising money for the statue in his honour, with a limited number of tickets now on sale to the public.