An error by Canvey defender Jon Kennedy gifted City a goal after half an hour, with Ben Burgess setting up Daniel Webb to score his second goal in three games.
Peter Taylor made seven changes at half time, while Paul Musselwhite, Nathan Peat, Marc Joseph and Damien Delaney played the whole 90 minutes.
There were no more goals in the second half, and City held on to the clean sheet record so far in pre-season to secure the 1-0 win.
City line-up: Musslewhite, Regan, Peat, Joseph, Delaney, Melton, Webb, Burgess, Williams, Keates, Hinds.
Run Extended to Three
Second half: Musselwhite, Peat, Joseph, Delaney, Ashbee, Price, Green, Allsopp, Forrester, Thelwell, Dawson.