Chester picked up the point they needed to secure their Football League status, relegating Mansfield in the process.
Goalkeeper John Danby was Chester's hero with a string of superb stops to deny Stockport, who were already sure of a place in the League Two play-offs.
He blocked shots from Adam Proudlock either side of half-time before Gareth Owen and Gary Dicker went close.
Danby saved his best for last, keeping out Anthony Pilkington's header from point-blank range as Chester held on.
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