The prolific Egypt forward brought up a century of Premier League goals in the win at Leeds United this month, becoming the 30th player to reach the landmark.
Two of those goals came in his time at Chelsea, but Salah now has a three-figure haul in the competition for the Reds after firing them into a 2-1 lead against the Bees, who subsequently equalised through Vitaly Janelt.
A VAR decision went in Salah's favour after he was initially given offside when converting Fabinho's excellent pass in the 54th minute.
The former Roma and Chelsea man reached the 100 mark in his 151st Premier League game for Liverpool to set the club record, getting there in one match fewer than it took the great Roger Hunt to achieve the feat.