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.
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.