The Egyptian scored a double in both halves to take the lead in the Golden Boot race ahead of Harry Kane and the winger also provided an assist for Roberto Firmino's clever flick after the break.
The Reds were looking to respond to their defeat to Manchester United last week and their resounding victory moves them to within a point of their rivals in second, edging ahead of Tottenham Hotspur - who played in the FA Cup this weekend - into third.
Salah took just four minutes to make his mark on the game as he shifted past Miguel Britos and finished a right-footed shot through goalkeeper Oscar Karnezis.
Salah then had a hand in the Reds' third goal; with just four minutes after the restart, he intelligently picked out the run of Firmino, who superbly flicked the ball between his legs and beyond Karnezis.
Watford once again stemmed the flow and with Pereyra they saw a wicked free kick smash against the crossbar. However it was Salah, who is having a prolific debut season, who found a second wind to score two additional goals in the final 12 minutes.
The Egyptian then attempted to set up substitute Danny Ings with a perfectly-weighted pass around the corner, however the ball fell back in Salah's path who turned home the rebound after Karnezis had denied the striker a first goal since 2015.
Liverpool: Karius; Gomez, Matip, Van Dijk, Robertson; Henderson, Can (Milner, 27'), Wijnaldum (Oxlade-Chamberlain, 71'); Mane, Salah, Firmino (Ings, 79')
Watford: Karnezis; Femenia, Mariappa, Prodl, Britos (Janmaat, 81'), Holebas; Pereyra, Doucoure, Capoue, Richarlison (Hughes, 65'); Deeney (Okaka, 70')
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