Lallana opened the scoring on 17 minutes before Ahmed Elmohamady was sent off for handling the ball on the line on the half-hour. Milner converted the spot-kick.
Sadio Mane made it 3-0 before half-time with a fierce drive.
David Meyler gave Hull hope, scoring from an early second-half corner but, less than a minute later, Coutinho curled in the fourth from 25 yards.
Milner completed the scoring with his second penalty on 71 minutes after Andrew Robertson had fouled Daniel Sturridge.