Steven Pressley's side had won three and drawn one of their previous four games at their makeshift stadium, but the visitors left with all three points thanks to goals in each half.
Clayton Donaldson got the first in the 22nd minute, getting on the end of Martin Fillo's pass to slot home.
Martin Taylor then doubled the advantage in the 68th minute, getting on the end of substitute Sam Saunders' cross.
The win lifts Brentford to 10th in the table, one point adrift of the top six after nine games.
Coventry, meanwhile, remain in the bottom four with four points, having been handed a 10-point deduction for entering administration before the start of the campaign.
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