On a prolific night across Europe which also saw a rampant Borussia Moenchengladbach hit six in Ukraine, the star individual performances came from Jota and Alassane Plea.
Portugal forward Jota joined Liverpool from Wolverhampton Wanderers in September and has wasted little time making an impact with seven goals from just five starts.
In Bergamo, against an Atalanta side who reached the quarter-finals last season, Jota was brought into the starting line-up in place of Roberto Firmino and required just 16 minutes to open the scoring.
Another emphatic finish allowed the 2019 Champions League winners to double their lead before the break, and Mohamed Salah then broke away to get the third just after the restart.
Salah set up Sadio Mane for Liverpool’s fourth before Jota got his hat-trick goal as the Premier League champions recorded their biggest win in Europe since beating Porto 5-0 away in February 2018.