Jurgen Klopp's side produced another top-class performance with their Egyptian forward Salah taking his tally for the league season to 13 goals in 14 games.
Liverpool are now averaging more than three goals per game having found the net 43 times so far in this campaign -- 10 more then the second most prolific side Chelsea.
A beautiful, curling shot from Jordan Henderson put Liverpool ahead in the ninth minute before the midfielder set up Salah with a fine through ball and Salah provided a clinical finish to make it 2-0.
The home side stuck at the task but Liverpool put the contest beyond doubt with Salah whisking the ball away from Seamus Coleman and providing the coolest of finishes.
"The message from the manager was that they will play physically strong and go 100% for every ball we just had to play our game and try to create chances, which we did," said Salah.
Liverpool are in third place on 31 points, a point behind Manchester City and two adrift of leaders Chelsea. Everton slipped to 14th place, five points above the relegation zone, and their fans protested against their club's board after booing the team at the final whistle.