Sadio Mane opened the scoring with a well-taken header before Georginio Wijnaldum scored the goal of the game with a delicious chip over the helpless Artur Boruc.
Mohamed Salah wrapped up all three points shortly after the break.
The Reds return to the top of the table, leapfrogging Manchester City, with the victory with the champions hosting Chelsea on Sunday.
Both teams have now played the same amount of the games.
Check out our player ratings in the gallery above
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