Gary Alexander opened the scoring from the penalty spot in the first half before debutant Shaleum Logan wrapped up the points with 14 minutes remaining.
Gavin Williams forced a decent early stop from home goalkeeper Richard Lee prior to Brentford's opener on the half hour. Nathan Jones was adjudged to have handled in the box and Alexander duly converted the spot-kick.
Jones had the chance to make amends before the break but fired wide from six yards, while Alexander almost grabbed his second of the game with a header which drifted wide.
Bees winger Myles Weston was forced off with an injury but it did not disrupt Brentford too much as summer signing Clayton Donaldson brought a superb diving stop from Jed Steer. Steer also did well to keep out a Marcel Eger shot from six yards but there was little he could do about the Bees' second goal as new-boy Logan slammed home from 12 yards after good work from Sam Saunders.
Williams almost pulled one back for the Glovers with a vicious 30-yard drive but Lee tipped the ball around the post.