No one seems able to keep up with Liverpool. Jurgen Klopp's team has won 16 of 17 league games, with one draw.
"The most important thing that you have to show in this period of the season is resilience, and that's what we showed again," Klopp said.
Salah made it four goals in two games as he followed up his Champions League double with another brace at Anfield.
Salah finished off a lightning counter-attack to give the hosts the lead in the 38th minute at Anfield and then made sure of the victory with a cheeky backheel from a tight angle in injury time.
It wasn't all so easy for Liverpool, though, even against a Watford side that is last in the standings. Only poor finishing prevented the visitors from taking at least a point in Nigel Pearson's first game in charge.
Striker Troy Deeney, Will Hughes, Abdoulaye Doucoure and Gerard Deulofeu all missed good chances to score for Watford.
Salah was as clinical as ever, though, taking his tally to nine league goals this season.
The only negative for Liverpool was Georginio Wijnaldum being forced off with an apparent hamstring problem, meaning he could miss the upcoming Club World Cup in Qatar.
Leicester saw their eight-game winning streak in the league ended by Norwich.
Jamie Vardy's streak of scoring in eight straight league games also ended after his header from a corner was ruled an own goal by Norwich keeper Tim Krul, who directed the ball into the net with his hand.
That goal equalised for Leicester in the 38th minute after Norwich striker Teemu Pukki had given the visitors a surprising lead in the 26th.
Vardy had a chance to score early in the second half when he rounded Krul but rolled the ball on to the outside of the post from a tight angle.
"We weren't quite at our level but we managed to get back and get a point," Leicester manager Brendan Rodgers said. "It was probably the right result, we didn't start so well and our passing was slow."
After surging up the table into the top four, Frank Lampard's Chelsea are in an alarming slump. Dan Gosling's 84th-minute goal gave Bournemouth the win, with Chelsea's grip on fourth suddenly looking shaky.
"We need more urgency in our play," Lampard said. "If you're an attacking player, get at people, do things that are positive, don't play safe. We play generally too safe through the game."
John Fleck scored twice as Sheffield United climbed into fifth by beating Aston Villa 2-0. Jack Grealish missed a penalty for Villa.
West Ham eased the pressure on manager Manuel Pellegrini with a 1-0 win at Southampton. Sebastian Haller scored the decisive goal in the 37th minute.
- AP
