Fabinho, Alex Oxlade-Chamberlain and substitute Takumi Minamino were all on target as the Bees slipped to a fourth defeat in five league games since Boxing Day.
Jurgen Klopp’s side still trail runaway leaders Manchester City by 11 points after the defending champions beat Chelsea on Saturday, though the Reds do have a game in hand to try to close the gap further.
The reverse fixture between the sides in west London produced one of the games of the season so far as they went toe-to-toe in an enthralling 3-3 draw.
Here, however, the home side were in the ascendancy throughout, eventually opening the scoring on the stroke of half-time when Trent Alexander-Arnold’s corner was allowed to bounce in the box and reach Fabinho at the far post, the Brazilian nodding home from close range.
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Bryan Mbeumo went closest to an equaliser as he fired just wide from Christian Norgaard’s clever reverse pass, while at the other end Diogo Jota struck the upright before also being denied one-on-one by Alvaro Fernandez.
Eventually, it was Oxlade-Chamberlain who gave Liverpool a deserved cushion as he showed great desire to get on the end of Andy Robertson’s cross to head past Fernandez.
The goal, just the second of the Englishman’s season, appeared timely given Sadio Mane and Mo Salah’s absences at the AFCON, but within minutes he was forced off injured after appearing to twist an ankle in the turf.
His replacement was Minamino and he made the points safe after Roberto Firmino pounced on Brentford’s attempts to play out from the back, pinching the ball from Norgaard before teeing up the Japanese international for a simple finish.