Sadio Mane headed the Reds into the lead on 31 minutes after Mohamed Salah had stood up a cross towards the back post.
Thiago Alcantara struck his first goal for the club as the game entered added time when he swept in from just outside of the area to make certain of the outcome.
The result moves Jürgen Klopp’s side to within six points of fourth-placed Leicester City, with a game in hand.
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Team news…
Liverpool made two changes from their last outing against Newcastle United on April 24 as Nathaniel Phillips and Rhys Williams came into defence.