It took only 13 minutes for the Reds to score the only decisive goal of the game in a move which was started and finished by Liverpool's Egyptian superstar.
He fired the ball home from point-blank range after some excellent link-up play involving Fabinho and Virgil van Dijk.
Aside from his century milestone, Salah became the first player in the club’s history to score in nine consecutive home games in all competitions, eclipsing Luis Suárez who managed to score in eight in a row in the 2013/14 season.
Jürgen Klopp’s side should have doubled their lead when Trent Alexander-Arnold played an exquisite pass into the path of Darwin Núñez, but the Uruguay international could not bring the ball under control at the decisive moment.
Chances were few and far between for the visitors, but Bryan Mbeumo was mightily unlucky to see his goal ruled out for offside after a superb run and finish as HT approached.
Thomas Frank’s men were facing a monumental task in a bid to leave Anfield with all three points, given the Reds had not lost in their previous 135 PL matches here when leading at the break.
Cody Gakpo had a golden opportunity to double the Reds’ advantage from Diogo Jota’s cross, but the ball ricocheted off the Dutchman’s shins.
However, to say it was all one-way traffic would be a disservice to the West Londoners. Their approach play was promising, although they lacked that clinical edge in the final third.
This was best summed up when Mathias Jensen brilliantly picked out Aaron Hickey at the far post, but the young Scot lost control of the ball at the vital moment.
Alexander-Arnold came close to scoring a second Liverpool goal with a long-range effort which was pushed to safety by David Raya, but the game petered out with Klopp’s men holding onto their lead with relative comfort.
The Reds moved to within one point of Manchester United in the UEFA Champions League places with this win, albeit having played two games more.
Meanwhile, this defeat for Brentford surely ends any slim hopes of European qualification with the Bees five points adrift of seventh-place Brighton & Hove Albion having played three matches more than the Seagulls.
Flashscore Man of the Match: Mohamed Salah (Liverpool)
