Second half goals from Diogo Jota, who bagged a brace and Mohamed Salah secured the deserved win.
Liverpool move up to fifth position on 49 points and are just two points behind fourth-placed Chelsea.
The defeat means Arsenal remain in 9th position on the log.
The Reds settled quicker and Fabinho drilled an early shot from range just wide before Mane had a deflected header easily saved.
A fine piece of skill from Roberto Firmino saw the Brazilian move into space and send a rasping shot wide just on the half-hour mark, but the best chance of the half saw James Milner steer an effort off-target from the edge of the box.
After the break, Arsenal initially tried to up the ante with a little more tempo about their play, but a Liverpool sub on the hour mark – Jota for Andy Robertson – and a tactical switch swung the game in their favour.
Jota powered in a header from a cross from the right just minutes after his entrance, before Salah beat Gabriel Magalhaes and finished between Bernd Leno’s legs to make it 2-0.
Jota then wrapped up matters with a close-range finish in the final 10 minutes.