The Bees coasted to victory with goals from Jay Tabb and Eddie Hutchinson either side of half-time as Brian Little's 100th game in charge of the Merseysiders turned into a nightmare.
Tabb got the home side off to the perfect start on 23 minutes when he ran onto a Paul Brooker through ball and scuffed his shot into the bottom corner.
Tranmere had come close early on through Chris Greenacre but it was all Brentford after that and Lloyd Owusu flashed a header just wide.
Allen's side should have wrapped up the points 11 minutes before the break when Isaiah Rankin led a four against one break only to hesitate too long and be caught in possession.
But Eddie Hutchinson made the game safe in the 50th minute when he headed home Kevin O'Connor's cross superbly.