Salah stars as Liverpool thrash Everton
Liverpool's Egyptian midfielder Mohamed Salah (R) runs past Everton's Irish defender Seamus Coleman to scores his team's third goal during the English Premier League football match between Everton and Liverpool at Goodison Park in Liverpool, north west England.–AFP
The Reds had won just one of their previous nine visits to Goodison, but were in complete control from the first whistle against Benitez's men, who have now taken just two points from the last 24 on offer in the Premier League.
Demarai Gray's strike gave the Toffees hope before the break.
But that was extinguished by another clinical Salah finish just after the hour mark as the Egyptian took his tally for the season to 19 goals in 19 games before Diogo Jota blasted home a fourth 12 minutes from time.
"It was for sure the best performance at Goodison since I have been at Liverpool," said Reds' boss Jurgen Klopp.
"We had some good games here but never as good or convincing as tonight.
"Tonight we showed we made a big step in our development. This is now our benchmark we have to reach when we play these type of games."
Benitez was an unpopular appointment among many of the Everton support before he had even taken charge of a game given his history as Champions League-winning coach for Liverpool during six years at Anfield.
A positive start had quelled some of the disquiet, but Everton are sinking fast towards a relegation battle with the fans in no doubt as to who is responsible.
The travelling Liverpool fans sang Benitez's name in ironic celebration, but he was met with a barrage of boos as he headed down the tunnel at full-time.
"I think anyone who could see the game we made too many mistakes and when you do that against a top side you pay for it," said Benitez.
Liverpool could have been out of sight inside 10 minutes as Joel Matip headed just wide before Salah turned Sadio Mane's dangerous cross over from close range and was then denied by a brilliant save from Jordan Pickford.
The opener arrived on nine minutes when Andy Robertson picked out Henderson in acres of space at the edge of the box and the England midfielder caressed the ball past Pickford.
The England goalkeeper was helpless again when Salah added to his collection of special goals in the past few months when he sprinted onto Henderson's perfect pass and bent the ball into the top corner.
Michael Keane nearly turned into his own net moments later as Everton were rocking.
But they and the crowd were given fresh belief seven minutes before the break when Richarlison picked out Gray in space between Matip and Alexander-Arnold to fire low past Allison Becker.
Everton at least made the game a contest for the first 20 minutes of the second period.
But one moment's hesitation from Seamus Coleman was pounced upon by Salah as he sprinted from halfway before slotting into the far corner.
"I expected him to do a mistake which he did," said Salah. "The game was tough at 2-1 but at 3-1 it becomes much better."
Jota then rounded off the scoring in style by drilling the ball high past Pickford as Liverpool scored four for the third consecutive league game.
Jurgen Klopp's men remain on the tails of leaders Chelsea and champions Manchester City, both of whom also won on Wednesday, with the top three separated by just two points.
Lionel Messi showed off his latest Ballon d'Or to Paris Saint-Germain supporters on Wednesday but the Argentinian had a quiet night as the Ligue 1 leaders were held to a 0-0 draw by Nice at the Parc des Princes.
The 34-year-old had been a pre-match doubt having reportedly picked up a stomach bug after going out to celebrate being named the best player in the world for the seventh time at a ceremony in Paris on Monday.
However, he started against Nice in a PSG side missing Neymar, who is expected to be sidelined for up to eight weeks with an ankle injury, the latest setback in the Brazilian's time in the French capital.
Angel Di Maria and Kylian Mbappe came closest to finding the net after the break for PSG, who had a huge let-off as Kasper Dolberg hit the post for Nice in the second half when it seemed easier to score.
"We created chances and I thought we deserved the three points," insisted PSG coach Mauricio Pochettino.
"We are improving little by little. We are top of Ligue 1 and through in the Champions League."
Messi has still managed just one Ligue 1 goal since moving to Paris in August from Barcelona, although he has also netted three times in the Champions League.
Gianluigi Donnarumma also showed off an award pre-match, the Italian displaying the Yashin Trophy he won at the Ballon d'Or gala for being the best goalkeeper of a year in which he starred in his country's Euro 2020 victory.
He did not have too much to do against a Nice team that defended superbly, although he did make one crucial stop from an Andy Delort header just after the half-hour mark.
"We were very, very well disciplined and I thought the draw was the right result," said Nice coach Christophe Galtier, who led Lille to the Ligue 1 title last season at PSG's expense.
France's Moto GP world champion Fabio Quartararo, who was born in Nice, appeared on the pitch before the match, taking the ceremonial kick-off before shaking hands with Messi and then embracing Mbappe.
- Marseille second -
Despite the draw, Pochettino's PSG side are 12 points clear at the top of the French table from Marseille, who climbed up to second with a 1-0 win at 10-man Nantes as Brazilian midfielder Gerson got their goal with a brilliant finish on the turn on the half-hour mark.
Marseille, who still have a game in hand following the abandonment of their recent match at Lyon, move above Rennes after the Brittany side went down 2-1 at home to defending champions Lille, Renato Sanches scoring what proved to be the winner.
Nice slip to fourth in the table, while fifth-placed Lens drew 2-2 at Clermont.
The big winners of the evening were Strasbourg, who crushed struggling Bordeaux 5-2 and sit sixth in the table, just above Monaco, 3-1 winners at Angers.
Meanwhile Lyon are languishing in mid-table after suffering a shock 2-1 defeat at home to Reims, with Hugo Ekitike scoring an injury time winner for the away side following a mistake by goalkeeper Anthony Lopes.
Lyon were forced to host the match behind closed doors as a punishment for the incidents in their last home game when Marseille's Dimitri Payet was struck on the head by a bottle of water thrown from the crowd.