The defeat, the eighth out of their last nine league games, came after two rash moves in a match were there was little to choose between the two sides.
A low key opening 20 minutes had seen little of note from either team, with efforts limited to two weak headers from David Artell and Stewart Drummond.
On the half-hour mark Chris Palmer was caught in possession by Derek Asamoah who played in Ryan Lowe but the Chester man delayed his effort allowing Dan Martin to get the vital block in.
Five minutes after the restart the home side had a great opportunity to take the lead when a cross from Ben Davies found its way to Lowe but he pulled his effort well wide.
Almost immediately the visitors made a quick break up field witch saw David Pipe in the clear but his right-foot shot was tipped aside by keeper Stephane Gillet.
On the hour mark Chester manager Keith Curle threw on striker Gregg Blundell in place of Marcus Richardson in an attempt to swing the game his side's way.
But it was the visitors who took the lead on 66 minutes when Luke Dimech needlessly handled the ball and captain Julien Baudet made no mistake from the spot.
A minute later it should have been 2-0 when substitute Steve Scoffham, who had been on the pitch only a matter of seconds, struck the post and the rebound fell to Eugene Dadi only four yards out but the striker somehow headed wide.
Late Chester pressure saw Drummond come close with a header, Lowe had an effort ruled off for offside before County were awarded a second penalty five minutes from time after a foul by Artell on Dadi.
Artell saw red for the offence while Dadi confirmed the win by dispatching the spot-kick past Gillet.