Hull, who had not lost an away game all season, were overrun, forced to play for an hour with 10 men after Ahmed Elmohamady was sent off for handling a Philippe Coutinho shot on the line with James Milner tucking away the resulting penalty.
The home side, already ahead through Adam Lallana, looked poised to score every time they pressed forward with Sadio Mane making it three before the break with his 11th goal in his last 13 league games for Southampton and Liverpool.
David Meyler's unlikely 51st-minute response for Hull was short-lived, Coutinho answering instantly with a superb fourth before Milner completed the rout with his second penalty after Daniel Sturridge had been fouled by Andrew Robertson.
(Reporting by Ian Chadband, editing by Ed Osmond)
