They were joined in the last 16 by Sevilla, Shakhtar Donetsk and Porto on the final matchday of the group stage.
A first Reds hat-trick from Philippe Coutinho, a brace from Sadio Mande and singles from Roberto Firmino and Mohamed Salah at Anfield ensured Liverpool topped Group E.
It means for the first time there are five EPL clubs in the last 16.
Sevilla drew 1-1 at eliminated Maribor to go through second ahead of Spartak.
Shakhtar defeated Group F winners Manchester City 2-1 to secure second place, with first-half goals by Brazilians Bernard and Ismaily.