The opening goal came in the sixth minute when Kevin Ellison cut in from the byline to cross for Richie Partridge to rifle home from eight yards out.
The visitors should have levelled matters in the 16th minute when Adam Birchall cut through the Chester defence but was denied by the legs of a sprawling Chester goalkeeper John Danby.
Chester doubled the advantage in the 40th minute with a spectacular half volley from Ellison who pounced on the ball on the edge of the box and hit a first-time effort from 20 yards out.
Ellison claimed his second after superbly bringing the ball down and striking a left-foot shot in off the post with 14 minutes remaining.
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