IT took the Blues 71 minutes to muster a shot on target as the Hatters cruised to a comfortable win.
There was an element of fortune about Stockport's first goal - but it was deserved on the balance of play.
Anthony Pilkington's shot from the edge of the area bounced out off the foot of the post, only to hit City keeper John Danby on the back of the head and roll into the net.
Any hopes of a City comeback were ended early in the second half when an unmarked Tony Dinning volleyed home at the far post from Adam Griffin's free kick.
There were only 19 minutes left on the clock when Simon Yeo had Chester's first meaningful effort on goal, but Stockport keeper Joe Lewis saved the striker's low shot. Soon after, sub Paul Rutherford headed over from point-blank range to cap a miserable afternoon for the Blues.
Star man: Paul Linwood.
Stockport: Lewis, Clare, Williams, Owen, Griffin, Poole (Proudlock 67), Dinning, Taylor, Pilkington, Elding, Dickinson (Nolan 85). Subs: Spencer, Tansey, Rowe.
Goals: Pilkington 22, Dinning 47.
Chester: Danby, Linwood, Artell, Bolland, Hessey (Vaughan 36), Sandwith, Hand, Bennett, Wilson (Rutherford 72), Yeo, Steele (Holroyd 36). Subs: Cronin, Meechan.
Attendance: 5,719 (343 away fans).
Referee: Uriah Rennie (South Yorkshire).