City's closest effort of the game was around the hour mark, as Stuart Taylor clawed Sam Collins's header from a corner onto the bar.
The Premiership side capped off the win with a second goal a minute from time after sloppy play left Craig Gardner one on one with Mark Lynch, and easily shrugged him off to score past Myhill.
City line-up (4-4-2): Boaz Myhill; Alton Thelwell, Michael Turner, Sam Collins (Mark Lynch, 69), Andy Dawson; Craig Fagan, Dean Marney (Keith Andrews, 85), John Welsh, Stuart Elliott; Ben Burgess (Billy Paynter, 58) Darryl Duffy (Stuart Green, 79).
Un-used subs: Thomas Woodhead, Michael Byron, Tom Matthews, Russell Fry.