Mohamed Salah scored the decisive goal in the 34th minute, finishing from a tight angle after he impressively turned Mario Rui and wriggled past Kalidou Koulibaly.
The Reds missed several chances to build on their lead against the Serie A side, with David Ospina doing well to deny Salah and Sadio Mane in the second half.
Mane also contrived to produce two inexplicable misses from close range, but Napoli were unable to punish their wastefulness in front of goal and will drop into the UEFA Europa League.
Unsung Milner as Vital to Liverpool as Salah
Salah will grab the headlines for his fine goal, and it's easy to see why:
The Egyptian is talismanic for the Reds, but James Milner—who supplied the pass for Salah—is similarly crucial to the cause.
As Opta's Duncan Alexander illustrated, the Englishman has been an impressive creative force in Europe for Liverpool:
On top of being an incisive contributor with his passing in the final third, the 32-year-old continues to shine as a tireless source of running in their engine room, helping them apply their press with work rate and intensity.
Football statistician Dave O'Brien shared his numbers from the first half against Napoli, as he impressed going forward and defensively:
Though much of his work often goes unheralded, Milner is one of the Reds' most influential players.
Klopp Right to Start Wijnaldum Ahead of Naby Keita
Reds boss Jurgen Klopp opted for a midfield three of Georginio Wijnaldum, Jordan Henderson and Milner, with Fabinho and Naby Keita on the bench.
Football writers Leanne Prescott and Jack Lusby weren't enamoured with the German's selection:
This is Anfield's Henry Jackson wasn't as quick to rush to judgement:
Keita and Fabinho have indeed been impressing in recent weeks, but Klopp's decision to put his faith in Wijnaldum—and to a slightly lesser extent Henderson—paid off.
The Dutchman played some excellent passes and looked to get forward where possible as well as helping out defensively.
Overall, he helped the Reds have 22 attempts on goal to Napoli's eight, and had those in front of him displayed better finishing, Liverpool could have won the match much more comfortably.
Dominic King of the Daily Mail singled out Wijnaldum for praise after the match:
Keita and Fabinho are growing in importance at Anfield, but the former has only returned to regular action recently after a spell out injured, while the latter has taken more time to adapt to Klopp's demands.
Wijnaldum in particular showed why Klopp was right to use him, and he may well play an important role for the Reds in the knockout phase, too.