Andy Scott’s side dominated possession for long periods but went down to goals in either half from Michael Twiss and Rene Howe.
Twiss opened the scoring with his first goal of the season after 23 minutes when he ran on to Fraser McLachlan’s long ball and volleyed past Ben Hamer.
Howe, the Shrimps’ top scorer, wrapped up the points with a goal from close range two minutes from time.
Brentford had their chances with Saturday’s hat-trick hero Jordan Rhodes seeing a first-minute effort well saved by Barry Roche. The teenager then forced the Morecambe stopper into another superb save after a shot on the turn in the 20th minute.
From there the Bees were defied superbly by a resolute home defence who earned Sammy McIlroy’s side their fifth home win of the season and a vital three points.