Mohamed Salah broke the deadlock four minutes into the second half with a neat flick into the bottom left corner from Trent Alexander-Arnold's cross.
Soon after, Roberto Firmino was hauled down in the area at the expense of a penalty - only for James Milner's effort to be pushed onto the post by Jasmin Handanovic.
But an emphatic finish from Emre Can and Daniel Sturridge's late strike assured three points for the Reds, who top their section ahead of Sevilla.
See how the game unfolded in photographs below...