The Reds took the lead as early as the fourth minute as Salah skinned one defender before poking the ball beyond Orestis Karnezis.
The Hornets struggled to get going as the hosts enjoyed most of the possession in the opening 20 minutes.
Jurgen Klopp was forced into an early change as James Milner replaced the injured Emre Can midway through the first half.
The change did not dent their approach though as they doubled their lead just before the break when Salah turned home Andy Robertson's fine cross.
It was 3-0 shortly after the break when the Egypt international skipped past a challenge before crossing for Roberto Firmino, who scored with a cheeky flick.
Watford showed no attacking intent as the second half continued as the third goal looked to knock the wind out of their sails.
The Reds bagged their fourth goal with 12 minutes remaining as Salah sent low strike into the far corner to complete his hat-trick.
Salah rounded off the scoring in the 85th minute as he smashed the ball home from close range after Danny Ings' initial strike was saved.