County started on the front foot and should have scored inside the first minute when a slip by Shaleum Logan let Francois Zoko in on goal, but Simon Moore saved the shot with his legs.
However, the pressure told after 20 minutes when Justin Kelly's low cross was turned into his own net by Bees defender Tony Craig.
Brentford hit back after 36 minutes when Marcello Trotta appeared to wait too long to play in Adam Forshaw.
But the linesman's flag stayed down and the instrumental midfielder tucked the ball away nicely under County keeper Bartosz Bialkowski.
The second half was a more tepid affair, but Donaldson won it for the visitors in the 88th minute when he headed in on the line after County failed to deal with a Brentford short-corner routine.