Mark Patterson blasted a 20 yarder against one upright, Gordon Armstrong hammered the rebound over an empty net and then a glancing header from Peter Swan struck the other post and Tony Battersby also wasted the rebound.
But despite their late rally Bury never did enough to threaten the victory which would have lifted them three places from next to bottom of the First Division.
Stockport, in the top third of the table, served early notice that they were prepared to tough it out. Kevin Cooper forced Dean Kiely to dive at his feet to save and Brett Angell was inches away from meeting an inviting cross .
The familiar story was repeated in the 16th minute when Alun Armstrong combined well with Paul Cook on County's left. A superb cross to the far post cleared the entire Bury defence and the unmarked Angell volleyed his 18th goal of the season.
Goal: Angell (17) 0-1.
Bury: Kiely; Gray, Armstrong, Daws, Lucketti, Butler, Andy Gray Jnr (Battersby, 75), Ellis, Swan, Johnrose (Rigby, 53), Patterson. Substitutes not used: Swailes.
Stockport County: Nixon; Connelly, Searle, Bennett, McIntosh, Gannon, Cook (Travis, 63), Angell, Armstrong, Cooper (Dinning, 84), Travis (Byrne, 84).
Referee: R Furnandiz (Doncaster).
Booking: Bury: Johnrose.
Man of the match: Angell.
Attendance: 5,699.Reuse content