Liverpool remain unbeaten in the Premier League this season after Sadio Mane scored his 100th goal for the club in a victory against Crystal Palace.
Jurgen Klopp's side 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.
Mane continues to haunt Palace
Sadio Mane has scored in nine consecutive matches against Crystal Palace in the Premier LeagueMane was one of six changes to Klopp's side from their win over AC Milan, and his return must have been an unpleasant sight for Palace fans.
Having scored twice against Palace on the final day of last season, Mane's opener on Saturday made him the first player to net in nine consecutive league matches against a single opponent.
It took his total to 13 against Palace in the Premier League - the most anyone has scored against them - and was the perfect way to notch up his 100th goal in all competitions for Liverpool.
Palace had attacking threat of their own from Wilfried Zaha - making his 250th Premier League appearance - but he was dealt with by the physicality of Fabinho and debutant Ibrahima Konate.
And while Palace continue to adapt and learn under new boss Patrick Vieira, they were given a humbling reminder of the ruthlessness of Liverpool's attacking quality.
Player of the match
Mohamed SalahMohamed Salah
Line-ups
Liverpool
Formation 4-3-3
1Alisson
7Milner5Konaté4van Dijk21Tsimikas
14Henderson3Fabinho6Thiago Alcántara
11Salah20Jota10Mané
1Alisson7Milner5Konaté4van Dijk21TsimikasBooked at 75mins14HendersonBooked at 40minsSubstituted forOrigiat 88'minutes3Fabinho6Thiago AlcántaraSubstituted forKeïtaat 62'minutes11SalahBooked at 79mins20JotaSubstituted forJonesat 76'minutes10ManéSubstitutes
8Keïta12Gomez15Oxlade-Chamberlain17Jones18Minamino26Robertson27Origi47Phillips62KelleherCrystal Palace
Formation 4-3-3
13Guaita
2Ward16Andersen6Guéhi3Mitchell
23Gallagher8Kouyaté18McArthur
9J Ayew20Benteke11Zaha
13Guaita2WardBooked at 83mins16Andersen6Guéhi3Mitchell23Gallagher8KouyatéSubstituted forOliseat 82'minutes18McArthurSubstituted forRiedewaldat 65'minutes9J Ayew20BentekeSubstituted forÉdouardat 65'minutes11ZahaSubstitutes
1Butland4Milivojevic5Tomkins7Olise12Hughes17Clyne22Édouard34Kelly44RiedewaldLive Text
Match ends, Liverpool 3, Crystal Palace 0.
Second Half ends, Liverpool 3, Crystal Palace 0.
Corner, Crystal Palace. Conceded by Virgil van Dijk.
Attempt blocked. Jordan Ayew (Crystal Palace) right footed shot from outside the box is blocked. Assisted by Jairo Riedewald.
Offside, Liverpool. Mohamed Salah tries a through ball, but Sadio Mané is caught offside.
Goal! Liverpool 3, Crystal Palace 0. Naby Keïta (Liverpool) left footed shot from outside the box to the top right corner following a corner.
Corner, Liverpool. Conceded by Joachim Andersen.
Attempt blocked. Curtis Jones (Liverpool) left footed shot from outside the box is blocked.
Substitution, Liverpool. Divock Origi replaces Jordan Henderson.
Corner, Liverpool. Conceded by Jairo Riedewald.
Foul by James Milner (Liverpool).
Conor Gallagher (Crystal Palace) wins a free kick on the left wing.
Joel Ward (Crystal Palace) is shown the yellow card.
Konstantinos Tsimikas (Liverpool) wins a free kick in the defensive half.
Foul by Joel Ward (Crystal Palace).
Substitution, Crystal Palace. Michael Olise replaces Cheikhou Kouyaté.
Attempt missed. Wilfried Zaha (Crystal Palace) right footed shot from the centre of the box misses to the left following a corner.
Corner, Crystal Palace. Conceded by Alisson.
Attempt saved. Odsonne Édouard (Crystal Palace) right footed shot from the centre of the box is saved in the bottom right corner.
Mohamed Salah (Liverpool) is shown the yellow card for excessive celebration.
Our coverage of your Premier League club is bigger and better than ever before - here's everything you need to know to make sure you never miss a moment