Jamie Forrester and David Reeves both limped off injured during the course of the half, with Phil Jevons and Steve Burton coming on to make rare appearances.
City looked to control the game more in the second half, and Phil Jevons hit the bar from Jon Otsemobor's cross after 20 minutes.
But the opening goal came 9 minutes from time when Dean Keates' corner was met by the head of Otsemobor to get his second goal in three games.
Victory was sealed soon later when Jevons was brought down inside the box after running onto Jon Walters' backheal. A line of City players all went for the ball to claim responsibility for the penalty, but it was the smallest man on the pitch and stand-in captain for the day, Dean Keates, who took it and buried it to Cartright's left.
The midfielder almost got another a minute later. Elliott and Jevons worked the ball to the back post, but Keates' flying header went wide.
City line-up (4-4-2): Fettis; Otsemobor, Joseph, Anderson, Delaney; Reeves (Burton 41), Melton, Keates, Elliott; Walters (Regan 90), Forrester (Jevons 30).
Un-used subs: Musselwhite, Donaldson.