Liverpool s Mohamed Salah, left, scores past Everton s goalkeeper Jordan Pickford his side s second goal during the English Premier League soccer match between Everton and Liverpool (AP)
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.
Stunning strikes from Jordan Henderson and Salah inside 20 minutes gave Everton a mountain to climb.
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.
Salah also has 13 Premier League goals to his name so far this season, four clear of nearest challenger Jamie Vardy of Leicester City.
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.
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.
Pickford was responsible for the cruciate ligament damage suffered by Virgil van Dijk in this fixture last season that derailed Liverpool's title defence and forced the Dutchman to miss the final seven months of the campaign.
The England goalkeeper was doing his best to frustrate the visitors once more as he then turned Trent Alexander-Arnold's powerful drive behind.
However, he was helpless 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.
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.
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