Midway through the first half Stuart Elliott was fouled inside the Wrexham area by Edwards, and so for the third successive home game City were awarded a penalty. However, skipper Dean Keates saw Andy Dibble save his shot.
10 minutes into the second half defender Jon Otsemobor got his third goal in four games for City. Keates' corner was flicked on by debutant Ben Burgess and Stuart Elliott headed the ball against the bar. But from the rebound Otsemobor blasted the ball into the net to make it 1-0.
However, City's lead lasted just 12 minutes before Lee Trundle went down inside the box and the visitors were awarded a dubious penalty. Andy Morrell showed Dean Keates how to take a spotkick, firmly despatching the ball to Alan Fettis' bottom-right.
Then with just under 10 minutes to go Morrell got the winning goal after Dennis Lawrence ghosted forwards and played in the division's top scorer to slide the ball past Fettis.
City line-up (4-3-3): Fettis; Otsemobor, Joseph, Anderson, Delaney; Reeves (Williams 79), Melton (Burton 10), Keates; Walters, Burgess, Elliott (Jevons 79).
Un-used subs: Musselwhite, Donaldson.