Brentford hung on for a first win in six games as Stockport continue to struggle following a 1-0 home defeat.
Charlie MacDonald's tap-in proved to be the difference on another miserable afternoon at Edgeley Park.
Jabo Ibehre missed two great chances for Stockport inside the opening 10 minutes as he somehow scooped a shot over the top from six yards, before planting a free header wide.
The visitors responded with Ben Strevens side-footing an angled shot narrowly wide, but back came Stockport and George Donnelly was thwarted by a smart save from Wojciech Szczesny.
On the half-hour mark Ibehre went close again, this time squeezing a low shot inches past the far post.
Brentford took the lead less than a minute into the second half. Myles Weston floated a cross towards the far post and there was MacDonald who tapped home from barely a yard out.
With eight minutes to go the woodwork came to Brentford's rescue as Donnelly's powerful angled shot bounced behind off the top of the crossbar.
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