Sadio Mane, with his 14th goal of the season, was also on the mark for Jurgen Klopp’s men, who have now lost just one of their last 20 league games.
But Salah, whose 32 goals match Newcastle’s entire tally in all competitions this season, again earned the plaudits after continuing a run that has seen him score in seven consecutive games.
Benitez, warmly welcomed by his former supporters at Anfield, saw Newcastle live dangerously before Liverpool finally took the lead in the 40th minute through Egypt international Salah.
Jordan Henderson benefitted from a fortunate ricochet and collected the ball just inside the opposition half. Alex Oxlade-Chamberlain took up the attack and, in turn, picked out Salah with a superb pass beyond the massed ranks of the Newcastle defence.
The striker moved the ball onto his left foot before beating Martin Dubravka with an unstoppable finish.
As has become his standard practice against the Premier League’s elite, Benitez sent Newcastle out in an ultra-defensive formation, yet the Magpies might still have gone in at the interval on level terms from their only noteworthy attack of the game.
A patient Newcastle build-up created space in the Liverpool defence and, after Mikel Merino had laid the ball back to Mohamed Diame, his excellent shot was curling into the top corner until Loris Karius leapt to make a superb save.
– Dominant Liverpool –
Liverpool would have only had themselves to blame had they failed to hold the lead until half-time, having dominated the first period.
After four minutes, and a mistake by Jamal Lascelles, Trent Alexander-Arnold’s centre ended up at the feet of Mane although a poor touch allowed the defender to make up for his error with a tackle.
Salah then latched onto Emre Can’s intelligent lobbed pass and lashed a volley into the side-netting before Can headed over and Dejan Lovren miscued a header straight at the keeper from six yards from a corner.
Liverpool pressure was mounting, with Virgil van Dijk responding slowly to a Salah corner and watching the ball pass untouched through the six-yard area with the goal gaping.
Mane had a shot deflected over, from a Roberto Firmino pullback, before the half-time whistle and, after the restart, Liverpool’s domination continued with the hosts appealing, in vain, for a penalty after a Salah shot appeared to hit the arm of Lascelles.
With Newcastle offering little more in the way of attacking ambition, the second Liverpool goal was inevitable and, when it came in the 55th minute, killed off any hope the visitors had of salvaging a point.
The goal was a simple affair, but devastatingly effective, as Liverpool carved a path through the middle of the Newcastle defence in a move started by Mane in his own half and continued by Can.
Finally, Firmino slipped through a perfectly-weighted pass which Mane struck, first time, past the diving Dubravka from 14 yards.
Despite going two down, Newcastle showed little more attacking ambition and when Jacob Murphy did have a rare glimpse of the Liverpool goal, he took the wrong option, shooting directly at Alexander-Arnold instead of trying to play in a team mate.
Finally, in the 77th minute, Kenedy’s deflected shot won a corner from which substitute Isaac Hayden headed just wide.
But Liverpool quickly re-established control, with Firmino’s deflected shot falling invitingly for Henderson whose first-time shot was deflected behind off Hayden for another corner.
In the closing minutes, as Liverpool coasted to an inevitable victory, it took a timely interception from Christian Atsu to stop Salah playing Can clean through on goal and, in the 93rd minute, Salah’s claim for a penalty was denied after a challenge by Lascelles.
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