A classy goal from Louis Hutton gave the Blues the lead early in the second half, but the home side fought hard to level the score before netting the winner in the dying moments.
There was little to separate the two teams as the game got underway in a fisrt half which saw few moments of real quality and only one clear cut chance apiece.
Kieran Kennedy was unlucky to have a header cleared off the line from a corner and at the other end; Erik Johansen made an outstanding low save from point blank range.
Shortly after the break, Hutton pounced on an opportunity to give City the lead, controlling the ball with his chest in between defenders before a controlled volley into the corner of the net.
Although Chester pushed on, City looked dangerous on the counter attack, playing particularly well down the left with Joree Intima almost doubling the Blues’ advantage.
As the game progressed, the home side upped the pressure, pumping long balls into the box and behind City’s defence.
Several corners and free kicks eventually paid off with two goals in quick succession meaning Chester were the victors on the day.