The Reds came into the contest in decent form following a 1-1 draw with Manchester City prior to the international break, and weren't at their best for portions of the game. But Sadio Mane, Philippe Coutinho and Divock Origi all scored to help the Reds extend their unbeaten streak against Everton to 14 matches across all competitions and 18 straight at Anfield.
It took only eight minutes for the hosts to open the scoring as Mane did well to work his way through several Everton defenders and finish with a deft strike into the bottom right corner.
Everton pulled back an equaliser against the run of play on 28 minutes and it was some poor set-piece defending that doomed Liverpool on this instance. The Reds failed to clear their lines following a corner kick and youngster Matthew Pennington was there to fire home his first Premier League goal.
But Liverpool took the lead back just a few minutes later through a spectacular individual effort from Coutinho. The little Brazilian avoided a tackle by defender Idrissa Gueye, cut inside to his right foot and unleashed a rocket into the top right corner, leaving Blues goalkeeper Joel Robles rooted to his spot.
Coutinho then played provider on Liverpool's third goal, slipping the ball perfectly into the path of Origi, and the Dutch international finished the move in style, blasting home to double the home side's advantage on the hour mark.
Liverpool continued to look for another goal late on and created more chances, notably when youngster Trent Alexander-Arnold forced a diving save from Robles late on. Everton pushed to get back into the match, but Liverpool comfortably saw out the final minutes to claim all three points.
The result sees the Reds (17-8-5) up to third place on 59 points, while Everton (14-8-8) remain in seventh place on 50 points.