After an opening half that saw the visitors largely keep the Reds at arm’s length and produce a series of good chances themselves, the hosts edged ahead two minutes into the second half courtesy of Alex Oxlade-Chamberlain’s low finish.
Roberto Firmino, who teed up the first goal, then created a second for Jordan Henderson, the captain sweetly side-footing in, and Mohamed Salah rounded off the scoring with a cute dink from the skipper’s assist and a 90th-minute conversion at close range.
Jürgen Klopp’s team therefore matched the second-longest unbeaten run in English top-flight history – 42 games – and equalled a Premier League record with their 20th consecutive home victory in the competition.