The West Brom striker came off the bench to hit two quality goals in a one-sided affair.
Harlee Dean broke the deadlock just before the half hour, getting across his man to head home Sam Saunders’ free kick with keeper Adam Collin stranded.
Saunders stretched the lead four minutes later, firing home from a tight angle beneath the luckless Collin.
And Berahino extended the lead with a smart volley minutes before the interval from Shaleum Logan’s right wing cross.
Paddy Madden forced a smart save from Bees substitute keeper Simon Moore just after the break, before Berahino put the result beyond doubt. He was on the end of a flowing Brentford counter attack to curl home a beauty from the edge of the box on 54 minutes.
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.