FC Halifax Town chief Darren Kelly felt his side were unfortunate not to pinch a draw.
The hosts went 2-0 ahead through James Roberts and Johnny Hunt before Jordan Burrow’s 11th goal of the season almost sparked a late fightback.
It was Halifax’s 12th defeat of the season and leaves them six points adrift of safety, but Kelly was encouraged by The Shaymen’s display.
“For large spells of the game I was very happy with our play,” he said. “There are bits we want to work on and improve on. We hate conceding goals and we aim for clean sheets but, overall, even though a defeat is a defeat, when we went 2-0 down we showed great character to come back.
“I thought for the majority of the second half we dominated and we really had a go, rather than the heads dropping like they’ve done in previous games. It’s something to build on. We showed effort with a bit of quality and we really took the game to Chester in the second half and we were unlucky not to come away with something.”
It is now 26 games without a clean sheet for Halifax after Roberts side-stepped Matty Brown following some hesitant defending before sweeping the ball past Matt Glennon.
Hunt doubled Chester’s lead when he marauded into the area after a super one-two with Ross Hannah before finishing confidently past Glennon.
Burrow was brilliantly denied by Jon Worsnop and then volleyed across goal before lashing in left-footed after he was set up by Shaun Tuton.
Chester: Worsnop, Higgins, Kay, Sharps, Hunt, Heneghan, Roberts (Richards 53), Mahon, Shaw, Rooney (Hughes 90), Hannah (Hobson 90). Unused substitutes: Forth, Chapell.
FC Halifax Town: Glennon, Bolton, Banton (Roberts 46), N Brown, M Brown, James, Wroe, Sadlier (Bencherif 83), McManus, Burrow, Hamilton (Tuton 46). Unused substitutes:Porter, Macdonald.
Referee: O Yates (Newcastle under Lyme).
Man of the match: Ben Heneghan.