Mohamed Salah's late goal gave Liverpool the lead before Darwin Nunez's stoppage-time sealer secured a 2-0 win over Napoli to give Jurgen Klopp victory in his 400th game in charge, ending the visitors' unbeaten start to the campaign.
Both sides were already assured of a place in the knockout stages of the competition, with only a four-goal winning margin enough to see Liverpool usurp Napoli in top spot.
The Reds managed two late strikes courtesy of Salah and Nunez, with Salah scrambling one over the line in the 85th minute after Alex Meret just about kept out substitute Nunez's header.
Nunez added a second from the final act of the match as Napoli, who earlier had a Leo Skiri Ostigard effort ruled out for offside, saw their unbeaten run ended at 17 matches.
Neither team could really find any rhythm in a quiet first half that took half an hour for the first shot on target to arrive, with Tanguy Ndombele forcing a save out of Alisson.
Liverpool attacked up the other end and only an Alex Meret stop prevented Thiago Alcantara from opening the scoring, shortly before Curtis Jones headed just over the crossbar.
Ostigard guided Khvicha Kvaratskhelia's free-kick delivery past Alisson eight minutes into the second period, but VAR – after a three-minute wait – ruled the defender was offside.
Kvaratskhelia then had a powerful volley saved by Alisson as Napoli, who had won their previous five group outings with a competition-high 20 goals, pushed for a winner.
A winner did arrive, albeit at the other end as Meret prevented Nunez's header from crossing the line, but Salah was there on the follow-up to poke over the line.
Nunez, introduced in the 73rd minute, added further gloss to the scoreline when tapping in Virgil van Dijk's goal-bound header from under the bar.