Liverpool created numerous chances against a resilient Palace before Mane pounced on a rebound at the back post in the first half.
Mohamed Salah doubled their lead with just over 10 minutes remaining when,
he smashed home a flick-on from a corner, before Naby Keita’s late curling strike made it 3-0.
Liverpool were wasteful in the first half as Diogo Jota fired over the bar from a few yards out in a glorious position,
while Thiago and Jordan Henderson were also denied by keeper Vicente Guaita.
Palace had started brightly – hitting the post twice in as many minutes as Liverpool,
failed to clear their lines in the box – but the hosts’ persistence eventually paid off.
In the end it was a comfortable victory that capped a good week for Liverpool at Anfield,
following their dramatic 3-2 win over AC Milan in the Champions League on Wednesday.
And it means they go top of the table with four wins from their opening five games,
while visitors Palace remain outside the top 10.