These two sides met in the Championship promotion play-off final last season with the Cottagers coming out triumphant 2-1 after extra-time at Wembley.
The Bees have had a reputation of dealing with top-flight sides in the cup competition this season.
After a 5-3 penalty shootout win over fellow Championship side Wycombe Wanderers in the first round, Brentford went on to dispatch Southampton and West Bromwich Albion in the second and third rounds, respectively, with a 2-0 win at St Mary’s and 7-6 penalty shootout win at the Hawthorns.
Thomas Frank’s men enjoyed home advantage at the Brentford Community Stadium this time and took the lead in the 37th minute through Finnish forward Marcus Forss.
They held on to this lead until the 62nd minute when Benrahma doubled the advantage with a close-range effort from a free-kick.
The West London outfit were not done and still had time for one more, again from Benrahma, in the 77th minute, this time a fierce strike from outside the penalty area.
It was clearly a terrible night for Fulham who fielded a strong line-up that included Franco-Mauritanian forward Aboubakar Kamara, DR Congo wideman Neeskens Kebano, Anglo-Nigerian attacker Josh Onomah and Ivory Coast midfielder Jean Michael Seri.
The Algeria international, who was named Man of the Match, was substituted a minute after completing his double for Fin Stevens. Apart from his goals, he also produced six successful dribbles from seven attempts, 45 touches and 11 accurate passes.
Wednesday’s victory marked the first time Benrahma made the Brentford starting XI this season, with his only other appearance being 17 minutes in their 1-1 Championship draw with Millwall.
The 25-year-old winger has been linked with a move away from Brentford all summer with the likes of Chelsea, Arsenal, Tottenham Hotspur and most recently Leeds United all rumoured to be interested in signing him.