A hat-trick from Sadio Mane and goals from Roberto Firmino and Mohamed Salah helped Jürgen Klopp's team rack up a handsome aggregate lead ahead of an Anfield return leg on March 6.
There was plenty to love about the Reds' performance at Estadio do Dragao - and here are five things that we particularly enjoyed...
Sadio joins an elite club
In scoring three times in Portugal, Mane became just the fourth Liverpool player to net a hat-trick in the Champions League proper.
Michael Owen, (Haka, 2001-02 and Spartak Moscow, 2002-03), Yossi Benayoun (Besiktas, 2007-08) and Philippe Coutinho (Spartak Moscow, earlier this season) are the only other players to have previously achieved the feat.