An Ibrahima Konate own goal and Yoane Wissa's header put the Bees in control, prompting angry Reds boss Jurgen Klopp to substitute key defender Virgil van Dijk at half-time.
Alex Oxlade-Chamberlain pulled one back but Bryan Mbeumo killed the Reds off as they lost more ground in the race for a top-four Premier League finish.
It was a case of no Ivan Toney, no problem for Brentford as Liverpool went the same way as Manchester United and Manchester City this season.
Despite Thomas Frank's upbeat assessment of the injury which forced Toney off on a stretcher at West Ham three days earlier, the Bees' 13-goal top scorer was not in the squad.
But his replacement, Wissa, had two goals ruled out for offside before he doubled the lead given to Brentford by Konate's error in a breakneck first half.
That was only after Darwin Nunez had added to his growing catalogue of wasted opportunities in front of goal.
The Uruguayan striker squandered another glorious chance to score after he was slipped in behind by Mohamed Salah.
Nunez took the ball round Bees goalkeeper David Raya and rolled it towards goal, only for Ben Mee to arrive in the nick of time to slide in and block.
At the other end, Wissa sent Mbeumo clean through on goal but the Cameroon frontman's shot was well saved by Alisson.
However, from the corner, the hosts took the lead when the ball ricocheted off the knee of France World Cup finalist Konate and squirmed past Alisson.
Mbeumo's corners continued to cause the visitors problems and Wissa put two of them into the net only for both goals to be chalked off.
However, the DR Congo winger made it third time lucky four minutes before half-time when he buried a superb header from Mathias Jensen's cross.
Alisson got a hand to the ball and scooped it out but referee Stuart Attwell's watch buzzed to confirm Wissa finally had his goal.
Klopp had seen enough of the shambles at the back and replaced Van Dijk with Joel Matip as one of three half-time changes.
The luckless Nunez did manage to find the net shortly after the restart after breaking through one-on-one with Raya, only for VAR to pull him up for offside.
Moments later, Liverpool made one count, Oxlade-Chamberlain glancing in a header from Trent Alexander-Arnold's tempting cross.
The Reds pressed for an equaliser but Raya did well to keep out a Fabinho shot and Konate headed wide.
And Brentford ended their hopes six minutes from time after Mbeumo brushed off a feeble challenge by Konate and tucked away the third.