Walters finished with a right-foot shot in first half stoppage time, before Simon Russell doubled the lead in the second half for a 2-0 win.
To read a full report of this match from Burnley site Clarets Mad click here.
City line-up: Musselwhite, Wiseman, Byron, Hinds, Peat; Fry (O'Neil 45), Tomlinson, Russell, Holt; Forrester, Walters.
Un-used subs: Matthews, Cattermole, Cooper, Donaldson.