Thomas Frank's side earned a measure of revenge for its EFL Championship play-off final defeat against Fulham last season as it swept aside its Premier League opponent in the fourth round.
Brentford took the lead eight minutes before half-time in its swish new stadium, with debutant Saman Ghoddos the creator.
The Iran midfielder took advantage when Jean Michael Seri lost possession, found space down the right and squared the ball for Finnish youngster Marcus Forss to slam home.
Said Benrahma, linked with a possible transfer to several Premier League clubs, doubled the Championship side's lead when the forward arrived at the far post to finish off Ethan Pinnock's header.
Making his first start of the season, Benrahma finished off Fulham with a superb strike from long-range in the 77th minute.
Tottenham Hotspur, Newcastle United, Manchester City, Manchester United and Everton reached the quarter-finals on Wednesday and Thursday (AEST).