Jon Walters headed home at his near post, highlighting the home team's vulnerability in defence, to give Stoke an early lead. But Liverpool responded positively after a disjointed start, with Adam Lallana and Roberto Firmino scoring before the break as the hosts took the lead.
Jurgen Klopp's men made sure of the win, which moves them one point ahead of third-placed Manchester City - whom they play on New Year's Eve - when Giannelli Imbula directed Divock Origi's cross into his own net.
Adding gloss to the scoreline was Daniel Sturridge, who scored his first league goal of the season - and Liverpool's 100th under manager Klopp.
Source: BBC Sports