Substitute Diogo Jota scored twice and Mohamed Salah added another to hand Jurgen Klopp's men a deserved three points over the underwhelming hosts.
Liverpool dominated possession and space for the majority of the first hour and Jota made that advantage count after 64 minutes when he headed home Trent Alexander-Arnold's cross to put the Reds in front.
Salah doubled the lead with an excellent solo effort four minutes later, shrugging off a Gabriel tackle on the right before driving inside and sliding a right-footed shot past Bernd Leno at the near post.
Jota collected his second in the 82nd minute after an Arsenal giveaway in their own half, sweeping home at the far post after running onto a loose ball.
The win gives Liverpool 49 points from 30 matches, two points behind Chelsea for the final Champions League spot. Arsenal remain stuck in ninth with 42 points.