It was an emphatic response to their defeat to Manchester United and moves the Reds to within a point of their rivals in second, leapfrogging Tottenham Hotspur into third.
Watford's three-at-the-back formation played into Liverpool's hands as it granted Salah and Sadio Mane space in behind the wing-backs to get at the visiting defence.
The Hornets survived the rest of Liverpool's early salvos without further damage and gradually grew into the game with Roberto Pereyra proving a useful outlet down the right.
Liverpool responded by countering ruthlessly and only a strong hand from Karnezis kept out Firmino after James Milner had set free Salah, who in turn released Firmino through the middle.
The hosts did extend their advantage before the break as Andy Robertson exchanged a one-two with Mane and crossed expertly for Salah to tap home at the back post.
Salah turned supplier four minutes after the restart as he intelligently picked out the run of Firmino, who skilfully flicked the ball between his legs and beyond Karnezis.
Watford's best spell came just after conceding their third as Jose Holebas shot into the side-netting from 25 yards and Pereyra whipped a vicous free kick against the crossbar.
It looked as though the Reds had taken their foot off the gas, but Salah, who is in the midst of the most prolific debut season of a Liverpool player, found a second wind to score twice more in the final 12 minutes.
The summer signing from Roma completed his first Liverpool hat-trick with a left-footed prod into the bottom corner, after his rapid changing of direction had seen him wriggle free of three Watford defenders.
Even when he tried to set up substitute Danny Ings with a perfectly-weighted pass around the corner, the ball fell to Salah who turned home the rebound after Karnezis had denied the striker a first goal since 2015.
It is the second successive season in which Liverpool have beaten Watford by a five-goal margin at Anfield.
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')