Chelsea were also shocked 1-0 at home by Bournemouth to see their lead over the chasing pack in fourth further cut, while Sheffield United moved into fifth with a 2-0 win over Aston Villa.
At Anfield, Liverpool kept their first clean sheet at home this season but only thanks to Watford's wastefulness in front of goal as the Hornets showed why they are the lowest scoring side in the league.
Abdoulaye Doucoure and Ismaila Sarr both failed to make a proper connection with the goal gaping in the first half and the 40-point gap between the sides in the table was shown only in the difference of quality in the finishing.
Salah struck twice as he rounded off a rapid Liverpool counter-attack from a Watford corner eight minutes before half-time.
The Egyptian then settled the home crowd's nerves a minute from time when he cheekily flicked home Divock Origi's mishit shot.
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"In December and January especially, you need to show resilience - that's the most important thing and we showed that," said coach Jurgen Klopp, whose side are seven games into a 15-match stretch across five competitions in 50 days.
"We had to fight, that's what we did and that's why we won."
Leicester will be Liverpool's next opponents in the Premier League on Boxing Day after the European champions head to Qatar for the Club World Cup.
The Foxes had the chance to cut the gap at the top to just five points ahead of that meeting had they beaten Norwich and Manchester City next weekend.
However, a club record run of eight straight Premier League wins for Brendan Rodgers's men came to an end against the Canaries.
Teemu Pukki broke clear and finished calmly for his ninth goal of the season to put the visitors in front.
Leicester levelled before the break when Jamie Vardy's header from James Maddison's corner was turned into his own net by Norwich goalkeeper Tim Krul, but the hosts could not press home their dominance in the second half.
"The players have been brilliant. When you are on that winning run you believe you are going to win every game but of course it does not work like that," said Rodgers.
"We were not 100 percent on it. We need to set the reset button."
Chelsea's hold on the fourth Champions League place could be down to as little as two points should Manchester United beat Everton on Sunday as their poor run continued.
Frank Lampard's men have now lost four of their last five Premier League games and had only themselves to blame as they had 18 shots on goal without finding a way past Aaron Ramsdale.
Bournemouth had lost five on the spin but got their reward for staying in the game when Dan Gosling skilfully flicked a loose ball over Kepa Arrizabalaga five minutes from time and VAR overturned a wrongly-raised offside flag against the midfielder.
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"Some responsibility is on the players to take the ball and have the balls to excite the fans," said Lampard after a fifth home defeat of the season.
"In front of our home fans it's evident we aren't playing well enough. We aren't taking our chances and we have given away some silly goals."
Sheffield United for now are the Blues' closest challengers as they moved ahead of United and Tottenham into fifth as John Fleck scored twice in the second half to inflict a 2-0 defeat on Aston Villa, while Jack Grealish missed a late penalty for the visitors.
At the other end of the table, West Ham eased the pressure on Manuel Pellegrini with a 1-0 win at fellow strugglers Southampton.
Sebastien Haller's first goal in nine games was the difference between the sides as the Hammers moved four points clear of the bottom three in 15th, while Southampton remain in the relegation zone.
Burnley were also 1-0 victors over Newcastle, thanks to Chris Wood's close-range finish in a game of few chances at Turf Moor.
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