Liverpool cut Manchester City's lead at the top of the Premier League to nine points with a 3-1 win at Crystal Palace on Sunday.
City could only draw 1-1 at Southampton on Saturday and Jurgen Klopp's men took advantage, winning the first of two games in hand they have on the defending champions.
Virgil van Dijk headed the visitors in front after eight minutes and Alex Oxlade-Chamberlain doubled the lead just after the half hour mark. Odsonne Edouard made it 2-1 just after the break but Fabinho's late penalty made the game safe.