The most recent clash between the Baggies and the Bees was at Griffin Park in March.
Albion eventually ran out as 1-0 winners in a fast-paced battle thanks to a Kyle Edwards goal. The young winger made a mazy run before chopping inside, dodging a duo of defenders and firing into the net.
Sam Johnstone had made a series of saves in the first half, twice denying Said Benrahma before foiling Julian Jeanvier and Yoann Barbet to keep the Baggies in the game.
The result meant Albion moved within seven points of the automatic promotion places, while Brentford stayed in 14th place.