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.
The Ukranian side finished ahed of Napoli who lost 2-1 at Feyenoord.
Two-time winners Porto secured second spot in Group G with a 5-2 win over Monaco in a game which ended 10-a-side.
Table-topping Besiktas won 2-1 at RB Leipzig.
Holders Real Madrid edged Borussia Dortmund 3-2 in Group H with Borja Mayoral, Cristiano Ronaldo and Lucas Vazquez on target.
Pierre-Emerick Aubameyang replied for the Germans.
Tottenham Hotspur, who defeated Apoel Nicosia 3-0 courtesy of goals from Fernando Llorente, Son Heung-Min and Georges-Kevin N'Koudou, topped the group.
Manchester United, Basel, Paris Saint-Germain, Bayern Munich, Roma, Chelsea, Barcelona, Juventus, Manchester City, Besiktas, Tottenham and Real Madrid had already secured their places in Monday's round of 16 draw.