Damien Delaney and Jon Walters had earlier squandered chances, while Alan Fettis denied Peter Duffield and Mark Angel. Mark Redfearn also saw his free kick deflected wide and Tom Bennett was off-target before Elliott popped up with his 9th goal of the season to seal the 1-0 win.
City line-up (4-4-2): Fettis; Joseph, Whittle, Anderson, Smith; Regan, Keates, Delaney, Elliott; Walters (Donaldson 69), Burgess.
Un-used subs: Musselwhite, Burton, Williams, Jevons.