Mohamed Salah's double means he has now scored 200 goals in English football
Salah opened the scoring just before the break, latching onto a pass from Darwin Nunez before placing a finish beyond Mark Flekken.
That was Salah's ninth Premier League goal of the season and his 10th arrived midway through the second half when he nodded in from Kostas Tsimikas' cross.
Salah - once again excellent on home soil - really should have had a hat-trick, having also volleyed over from a superb Trent Alexander-Arnold cross just before half-time.
Diogo Jota then rounded off another dominant home display with a thumping strike.
Brentford's best chance had come in the first half, when Bryan Mbeumo raced through on goal but his chipped effort was tame and cleared off the line by Alexander-Arnold.
The victory means Liverpool have 27 points and move ahead of Arsenal on goal difference, while Brentford are 10th.
-- Courtesy of BBC Sport