Mohamed Salah’s ninth-minute goal was the difference between the teams during a first half of few real opportunities at either end.
A much livelier second period followed and Sadio Mane’s thunderous finish gave the Reds a cushion that was quickly wiped out – as Callum Peterson tapped in a low cross.
But substitute Xherdan Shaqiri clinically restored the cushion – and opened his account for the club – with six minutes to go and Mane added further gloss to the scoreline with a delicate chip moments later.
And the eventually emphatic win sent Liverpool ahead of Manchester City, who are not in action until a clash with Tottenham Hotspur on Monday night.