Skipper Matt Oakley blazed the final effort over from 18 yards in injury time.
After a cagey opening, it was 18 minutes before any side produced a shot on goal.
City's Steve Howard tried a low effort from 18 yards, but it was comfortably blocked by Stockport defender Michael Raynes.
Stockport's summer signing Carl Baker then saw a deflected shot easily gathered by keeper Paul Henderson.
Howard dived in to head Aleksander Tunchev's cross well wide, then on 32 minutes City right-back Kerrea Gilbert went close when his cross-cum-shot from the right just dropped inches past the far post.
City wideman Max Gradel was booked shortly before the interval after petulantly booting the ball into the stand after giving a throw-in away, before Stockport came agonisingly close in stoppage time.
Raynes headed the ball into Peter Thompson's path only for his shot to rebound out off the base of a post before the loose ball was pounced upon by Henderson.
City started the second period purposefully and four minutes in Matty Fryatt twice went close within a matter of seconds.
Firstly a shot was blocked by Dominic Blizzard, then he blazed a loose ball over from 15 yards.
On 55 minutes, Fryatt was denied by a super point-blank save from Owain Fon Williams.
Stockport responded with sub Anthony Pilkington forcing a save out of Henderson, but by now Fryatt was again looking dangerous as he twisted and turned before shooting over the bar from an angle.
Fon Williams again did well on 75 minutes when his low one-handed save kept out Andy Gray's goalbound shot, then City sub Paul Dickov glanced a header narrowly wide from Lloyd Dyer's measured cross.