An even first half ended all square as Alex Oxlade-Chamberlain's opener was cancelled out by Leroy Sane, but the Reds took it up a gear in the second as Sadio Mane, Roberto Firmino and Mohamed Salah all netted.
City launched a late fightback through Bernardo Silva and Ilkay Gundogan but were held off as Jürgen Klopp's team claimed a big three points.
Check out the best of the pictures from the game below.
Images brought to you by Western Union, official principal partner of Liverpool FC