The home side were all over City and McCulloch had further chances to extend the lead but failed to convert.
City then edged their way into the game before half time, and Danny Allsopp had a great chance but clipped the top of the bar from Jason Price's cutback.
Wigan hit the cross bar twice in the space of a minute shortly after the break but City were let off, while Stuart Elliott headed a corner just wide. Stuart Green was then denied a goal for a very tight offside call.
City continued to press but failed to carve out any clear chances, and Dean Keates and Steve Melton were brought on in the 77th minute.
However, the game was up when Jason Jarrett ended a counter attack move by receiving a right wing cross and lashing it past Fettis four minutes from time.
City line-up (4-4-2): Fettis; Thelwell, Whittle, Hinds, Delaney; Price (Melton 77), Green, Ashbee, Elliott (Keates 77); Burgess, Allsopp.
Un-used subs: Musselwhite, Holt, Forrester.