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.
Chester: Danby, James Vaughan, Kelly, Linwood, Wilson, Partridge (Grant 57), Roberts, Hughes, Sandwith, Murphy, McManus (Rutherford 57).
Subs Not Used: Palethorpe, Rule, Mitchell.
Booked: Hughes, Roberts, James Vaughan.
Stockport: Logan, Taylor (Turnbull 43), Owen, James Smith, McNulty, Pilkington, Blizzard, Dicker, Rowe, Dickinson (Proudlock 28), Lowe (Gleeson 45).
Subs Not Used: Ruddy, Rose.
Booked: Owen, Lowe, Pilkington.
Att: 3,060
Ref: Keith Woolmer (Northamptonshire).
Chester: Danby, James Vaughan, Kelly, Linwood, Wilson, Partridge (Grant 57), Roberts, Hughes, Sandwith, Murphy, McManus (Rutherford 57).
Subs Not Used: Palethorpe, Rule, Mitchell.
Booked: Hughes, Roberts, James Vaughan.
Stockport: Logan, Taylor (Turnbull 43), Owen, James Smith, McNulty, Pilkington, Blizzard, Dicker, Rowe, Dickinson (Proudlock 28), Lowe (Gleeson 45).
Subs Not Used: Ruddy, Rose.
Booked: Owen, Lowe, Pilkington.
Att: 3,060
Ref: Keith Woolmer (Northamptonshire).