Chester earned a third straight league win at fellow relegation contenders Grays to knock another three points off their crippling 25-point deduction.
Chester striker Michael Coulson opened the scoring, rifling an 18-yard drive into the top-left corner.
Fola Onibuje headed Grays level from close range via Danny Bunce's corner.
Nick Chadwick put City back in front by half-time before adding a clinching late second from Coulson's cross for his seventh goal of the season.
Chester are now on -4, within two wins of getting into positive figures.
City boss Jim Harvey said: "There is no reason, with performances like this, why we shouldn't survive in the Blue Square Premier.
"The three wins on the bounce are down to a tenacity and hunger, which we want to keep going.
"The question I was asking myself all week was could we follow up the superb performance we put in against Wimbledon last week, and they did."
Grays Athletic: Edwards, Davis (Asllani 76), Mawer, Uddin, Bunce, Graham (Pendergast 60), Robson, Leahy (Agumbar 55),Poole, Slabber, Onibuje.
Subs Not Used: Charge, Rnkovic.
Booked: Robson.
Goals: Onibuje 32.
Chester: Danby, Roberts, Ryan, Flynn, Meynell (Wilkinson 85),Coulson (Kay 90), Owen, Keltie, Ashton, Chadwick (Blundell 80), Beesley.
Subs Not Used: Murphy, Rule.
Goals: Coulson 30, Chadwick 44, 78.
Att: 480
Ref: J Farries (Oxfordshire).
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