Jurgen Klopp’s side were superb throughout as they maintained their 100% start in the competition.
Mohamed Salah’s prodded finish set them on their way at the Estadio do Dragao, which once again proved a happy hunting ground.
And with memories of 4-1 and 5-0 victories in recent campaigns fresh in the mind they delivered a performance brimming with pace, precision and energy.
Sadio Mane extended their lead on the stroke of half-time with a back-post tap in and with the Reds wearing black armbands to mourn the death of Roger Hunt, fittingly Salah – their modern-day equivalent – contributed his second with a clinical finish into the bottom right corner.
Mehdi Taremi’s header briefly gave the hosts heart but Roberto Firmino added the fourth for Liverpool with home goalkeeper Diogo Costa stranded after woefully charging up the pitch to attempt to clear.
And the Brazilian rounded off a comprehensive victory late on after pouncing on a rebound from Curtis Jones’ volley.