His summer arrival for £38million, at the time a club record, was questioned by critics after his disappointing spell at Chelsea but on this form he is looking an absolute bargain.
Both his first-half goals had a touch of class and his constant threat had visitors backpedalling for 80 minutes before his departure to a standing ovation - by which time Philippe Coutinho had added the third goal.
Having edged one ahead of the likes of Harry Kane and Sergio Aguero, both strikers, Salah is racking up some impressive numbers.
The 25-year-old's double took him to nine goals in his first 12 Premier League matches, breaking the club's previous best held by Robbie Fowler - the man affectionately hailed as God by the Kop for his goal-scoring exploits.
Salah's overall statistics are equally impressive with 14 goals, all from open play, in 18 matches and three assists. Last season Philippe Coutinho was the club's leading scorer with 14.
And this from a winger whose finishing has, at times this season, still been criticised.
But Liverpool are far from a one-man team as with Salah on one wing, the equally-pacy Sadio Mane on the other, Roberto Firmino running the channels as the nominal centre-forward and Coutinho pulling the strings in midfield Jurgen Klopp's team have all the ingredients to be devastating.
As they approach a critical part of the season everything appears to finally be aligning for Liverpool having overcome most of their injury problems - albeit defender Joel Matip missed this game with a thigh problem - with the fit-again Adam Lallana not even able to make the bench against his former side.
Many inside Anfield would have been closely watching Saints centre-back Virgil van Dijk, the man Klopp believes is the missing link for his defence, but it quickly became apparent there was more compelling action on Liverpool's flanks.
The defender's mis-control almost put Trent Alexander-Arnold in for the first goal early on before Salah, who had already volleyed wastefully wide, ended his club's 459-minute goal drought against Southampton with a superb curling effort from Georginio Wijnaldum's lay-off just past the half-hour.
His second was just as brilliant. Van Dijk half-heartedly and somewhat inexplicably stepped forward with Coutinho on the ball and the Brazil international's outside-of-the-foot pass allowed Salah to run in behind and clip past Fraser Forster.
Salah continued to torment after the break with one scintillating counter-attack messed up by Alberto Moreno's clumsiness in the penalty area.
Coutinho stabbed wide a good chance before making amends by smashing home Firmino's parried shot in the 68th minute.
Southampton rarely looked like preventing Liverpool keeping a fifth clean sheet in six home league matches, which almost went unnoticed in the celebration of their exhilarating attacking play.