Firmino, Salah, Takumi Minamino, Sadio Mane, and Jordan Henderson were all on the scoresheet as the champions overwhelmed Roy Hodgson’s side with a stunning away performance.
Liverpool raced into the lead in the third minute as Mane set up Minamino, who coolly found the bottom corner.
And the Senegal international then doubled the advantage in the 35th minute after a superb turn, before Firmino tapped home to round off a brilliant counter-attack on the stroke of half-time.
Captain Henderson curled in a fourth just after the restart before Firmino added his second after good work from Salah.
Salah headed home a sixth with nine minutes remaining, before doubling his personal tally with a brilliant individual effort moments later.
The Egyptian forward rounded off brilliant team performance, as a scintillating Liverpool ensured they would be top at Christmas for the third consecutive season.