Liverpool dominated early on, scoring a fine opening goal on the counter attack when Luis Diaz arrowed his first of the season into the top corner with 13 minutes on the clock.
Brentford responded well, going close with two short-range headers either side of halftime, but Mohamed Salah ended the visitors' hopes of taking anything from their trip to Anfield with a second goal 20 minutes from time.
Dutchman Slot now has two 2-0 wins from two games as he undertakes the difficult task of replacing Juergen Klopp as Liverpool boss, with a testing trip to Manchester United up next.
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