Mohamed Salah scored a 38th-minute opener for the nervy Reds, but Abdoulaye Doucoure and Ismaila Sarr missed excellent chances to find the net for Watford either side of the goal. Sadio Mane had a goal chalked off for offside after a VAR review in the second half, but Liverpool ultimately held on when Salah cheekily flicked over the line in the final minute.
Victory also means Liverpool are now unbeaten in 34 games in England's top flight, while the Hornets remain six points shy of safety after Nigel Pearson's first match in charge.
The disparity in league places counted for little early on when Watford proceeded to dictate play at the home of the would-be champions. It was the visitors moving the ball quickly and intelligently on the flanks, regularly getting Gerard Deulofeu and the lively Sarr involved.
Pullbacks from wide areas were causing Liverpool problems, and the Hornets blew an outstanding chance to go in front when Doucoure inexplicably kicked the ground when meeting a low cross delivered to the penalty spot.
Any decent contact from the midfield powerhouse surely would have resulted in a goal and a shock lead. Instead, fate decreed Watford would be punished for Doucoure's profligacy.
So it proved when Salah broke clear at the other end of the pitch and curled in the opener.
The Egyptian has been Liverpool's attacking talisman since returning to England's top flight in 2017. Salah's status was cemented by his latest goal taking him past another famous Reds finisher:
Astonishingly, Watford should have been level mere moments later, but the visitors spurned another terrific chance from inside the air. This time it was Sarr, who hit mostly air with Liverpool goalkeeper Alisson Becker stranded out of position:
Liverpool barely deserved a slender lead at the start of the second half, but the hosts thought they had done enough to double their tally six minutes after the restart.
Sadio Mane had applied the finishing touch by getting his head to a Xherdan Shaqiri cross. However, VAR correctly judged Liverpool's No. 10 was marginally offside:
Tight margins were playing on Liverpool minds, with the usually error-free Virgil van Dijk nearly beating Alisson with a misplaced pass back. Deulofeu then swung the resulting corner on to the post with tension building among the home faithful.
It was measure of how much Jurgen Klopp was feeling the pressure that he hooked Roberto Firmino for Divock Origi and ordered his team to reshuffle into a defensive 4-5-1 shape.
Even so, Liverpool still had enough impetus to score a second after Origi's dragged shot fell kindly for Salah, who wasn't about to halt his run of punishing Watford:
Liverpool will play better this season, but securing a win and keeping a rare clean sheet on an off day proves this squad has the resolve to match its quality. The combination usually leads to titles.
Liverpool are away to Aston Villa in the quarter-final of the 2019/20 Carabao Cup on Tuesday, a day before beginning action in this year's FIFA Club World Cup.
The Hornets won't return to action until Sunday, December 22 when they host Manchester United at Vicarage Road.