Brentford struck four goals away from home to move up to third in the Championship as they inflicted a fifth defeat in six games on 10-man Bristol City.
Defender Ashley Williams was shown a straight red card inside the first 15 minutes for halting Ollie Watkins's run towards goal, after Bryan Mbeumo had poked in an early opener after sloppy City defending.
Said Benrahma doubled the lead on the rebound after Watkins' shot was saved and then the Bees took full control with a dominant second-half display.
The lively Watkins slotted in two late goals of his own from close range in the closing stages to add deserved gloss to an impressive away victory.
Brentford, who had not won on their travels since 9 November, moved above Fulham in the table as their west London rivals were beaten 2-1 at home by Reading.
The visitors' win at Ashton Gate also lifted them to within eight points of the automatic promotion places, ahead of the meeting of the top two, Leeds and West Brom, later on Wednesday at the Hawthorns.
Thomas Frank's men could have scored more goals but Daniel Bentley saved well from Ethan Pinnock's header with 11 minutes to go, after Watkins had earlier headed narrowly wide across the face of goal.
Bristol City, who were fourth as recently as 7 December, have slipped to 11th having lost at home for the third time in four outings.
Boos rang around Ashton Gate as the hosts' head coach Lee Johnson replaced winger Niclas Eliasson with centre-back Taylor Moore on 28 minutes with his side enduring a thoroughly unhappy start to 2020.
Johnson's afternoon got worse when he was shown a straight red card after the final whistle had gone, as he appeared to get involved in an altercation with Frank, with the pair exchanging angry words.
The Robins boss said he will appeal against the red card.
"All that happened was that Thomas grabbed my cuff as we were talking and I ripped it away," Johnson said.
"Hopefully one of the cameras was filming at the right angle to prove my case. I have huge respect for Thomas and we will be having a drink together in my office."
Johnson also said that while it may "seem strange" he felt "quite positive" about the performance.
"You cannot go a goal and a man down so early to a team like Brentford and our sloppy start to the match did concern me," he said.
"Ashley has apologised to the other players. He wasn't the only one to make mistakes early on and we will have to look at that.
"But after their second goal I felt the players gave everything and we created some good situations. With the right additions this month, we can be up there when it matters."
Brentford boss Frank readily admits he expects Watkins' form has caught the attention of other clubs, but the Dane remains hopeful that he will stay with the Bees.
"Of course Ollie's form will attract interest, but I see no reason why he should want to leave this month," Frank said.
"Sometimes in life you find yourself working at a special place and that is what we have at the moment.
"A player as good as Ollie will get more than one opportunity and I am very hopeful he will remain with us until the summer at least."