Jon Walters opened the scoring at Anfield, but Jurgen Klopp’s side hit back through Adam Lallana, Roberto Firmino, a Giannelli Imbula own goal and Daniel Sturridge.
Jon Walters opened the scoring on Merseyside inside 12 minutes, with his glancing header from an Erik Pieters delivery parried over the line by Simon Mignolet.
Parity was restored in the 35th minute when Sadio Mane’s centre ricocheted into the path of Adam Lallana off ex-Reds defender Glen Johnson and the England international fired home from a tight angle.
Roberto Firmino then completed the turnaround for the hosts shortly before half-time as he was allowed to spin inside the area and drill a low left-footed effort in off the post.
The points were wrapped up by Jurgen Klopp’s side on 59 minutes as Giannelli Imbula, stretching in front of Mane, prodded a Divock Origi cross into his own net.
Liverpool were not done there, though, as Daniel Sturridge netted his first Premier League goal of the season – latching onto a blind back-pass from Ryan Shawcross to round Lee Grant and roll into an empty net.