Shrewsbury saw off their opponents with four goals in the second half. Trevor Challis headed the first goal before the break, before goals from Darby, Challis again, Rodgers and a Town first for John Grant wrapped up the game for the league side.
Ben Smith made his debut in behind the strikers, as Town again used a 3-5-2 formation.
Dave Cooke, assistant boss, told ShrewsWeb: 'I thought we controlled the game from start to finish and it was a good game for us to play, capped off with some good goals towards the end'.
Of debutant Smith he added: 'Ben Smith is a quality player and if we do play that system with him in the hole then he can make things happen.'
Town physio Dean Spink said that Colin Cramb was progressing well with his knee injury, and that Dave Edwards should figure on the tour of Devon after recovering from a shoulder problem.