Stockport's Liam Dickinson struck five minutes from time to deny Football League new boys Dagenham a point.
County deserved the win as they controlled the first half but saw Adam Griffin denied by Daggers keeper Tony Roberts and David Poole volley wide.
Jon Nurse came closest for Dagenham but he directed his free header wide while at the other end Roberts kept out Anthony Elding and Poole.
Roberts was finally broken when Dickinson struck home at the near post.
Stockport: Logan, Tierney, Owen, Williams, Smith,,Griffin (Dickinson 67), Taylor, Dicker (Blizzard 86), Poole (Proudlock 63), Elding, McNeil.
Subs Not Used: Chris Adamson, Tansey.
Goals: Dickinson 85.
Dag & Red: Roberts, Foster , Uddin, Boardman, Griffiths, Saunders (Strevens 74), Southam, Rainford, Sloma (Huke 62), Benson (Moore 80), Nurse.
Subs Not Used: Thompson, Okuonghae.
Ref: G Salisbury (Lancashire).