Three goals in the first 30 minutes saw Martin Allen's side secure a comfortable 3-0 win at Griffin Park.
The Bees flew out the traps and took only four minutes to break the deadlock when Michael Dobson headed in Stuart Talbot's corner.
Stockport nearly found themselves back on level terms immediately only for Warren Feeney to rattle the woodwork with a header from a Mark Bridge-Wilkinson cross.
It then got worse for County when they conceded a killer second goal. Isaiah Rankin dispossessed John Hardaker before unselfishly cutting the ball back for John Salako to coolly slotted home.
Feeney replied by blazing over from an acute angle before Brentford scored a third on the half hour mark.
A long throw in from the left hand side resulted in the ball finding Deon Burton who has no problem prodding it home.
County boss Sammy Mcllroy made a double substitution at half time to try and change the fortunes of his side but it was the home team who kept on carving out chances with both Rankin and Burton looking to add to their tally for the afternoon.
Although County posed more of a threat after the break, Brentford keeper Stuat Nelson was rarely tested and while Brentford will be looking to make two wins in two days on Monday, Mcllroy will have plenty to do for the visit of Tranmere.