His first of the evening was curled exquisitely past Alisson, while the Brazilian was equally powerless to stop him doubling Liverpool's lead minutes later with a fine dinked finish.
Salah then went on to assist both Sadio Mane and Roberto Firmino after the break, before being withdrawn by manager Jurgen Klopp shortly after Firmino briefly put Liverpool five goals ahead .
And with a total of 43 goals this season, the striker has overtaken Cristiano Ronaldo as the top scorer on the continent in all competitions as we enter the final stages of the season.
Salah's 43 have come in just 47 games, although Ronaldo bests that strike-rate with an incredible ratio of 42 in 39 appearances.
Lorenzo Insigne of Napoli completes the podium with 41 goals in 45 games, while Lionel Messi lies fourth having netted 40 in 50.
Ronaldo nevertheless continues to lead the way in the Champions League, scoring 15 to Salah's 10.
The Real Madrid star will have the chance to reassert his leadership in the scoring charts on Wednesday, when Madrid travel to the Allianz Arena to face Bayern in the second semi-final first leg.