The holders, who lifted the trophy for a sixth time in Madrid on June 1, were level until the 82nd minute when Dries Mertens fired a penalty past Adrian after Andrew Robertson had fouled Jose Callejon.
A rare Virgil van Dijk error then gifted Fernando Llorente a second in the 92nd minute as Napoli beat Liverpool at home for the second consecutive season, leaving the Reds three points behind their opponents and Red Bull Salzburg after matchday one in Group E.
Considering Napoli began their campaign with back-to-back 4-3 scorelines and Liverpool had only kept one clean sheet all season, it was perhaps unsurprising that the game quickly settled into a free-flowing, end-to-end attacking rhythm.
It certainly did not look as though the two sides were about to play out a goalless 80 minutes or so, and Napoli even had the ball in the back of the net in the seventh minute.
Fabian had another chance after quarter of an hour when he found space at the back post, but he opted to put the ball back across the face of goal when he might have shot, allowing Virgil Vijk to hack it away from danger.
Moments later Roberto Firmino clipped a pass through for Mohamed Salah, who got the wrong side of Kalidou Koulibaly but refused to go down under the centre-back's clumsy challenge inside the box. The Egyptian's shot was eventually blocked, though, while James Milner blasted a follow-up effort well off target on his 100th European appearance.
Salah then dragged a 25-yard effort wide of the near post before a timely interception from Kostas Manolas prevented Milner from finding the winger in a position from which he would have expected to score.
Arguably Liverpool's best chance of the half came from the resulting corner when Firmino suddenly found himself unmarked in the box, only to flick his header narrowly wide of the target when he should have done better.
The Brazilian was almost made to rue that miss four minutes into the second half when Mertens cushioned a volley towards goal and looked certain to have scored until Adrian pulled off a world-class stop to tip the ball wide - an early contender for save of the season.
It marked a quick start to the half for the hosts, although Liverpool were always a threat on the break and should have made more of a two-on-one situation when Mane and Salah were up against Mario Rui, who successfully delayed the pass which was then too heavy when it arrived.
Salah did get the chance to go for goal shortly after the hour mark when Manolas horribly sliced a clearance straight to the Egyptian inside the area, but his powerful low first-time effort was brilliantly tipped wide by Meret.
Meret was called upon again with just over 15 minutes remaining when some smart interchange between Mane and Firmino released the former into the box, where he put his finish too close to the Napoli keeper.
The defining moment of the contest came 10 minutes from time when Callejon cut inside from the right and got his toe to the ball before Robertson, going down under the Liverpool man's challenge. The referee pointed to the spot and VAR upheld the decision, leaving Mertens to blast his penalty past Adrian despite the Spaniard getting a hand to the ball.
It was the second time in as many years that the visitors had conceded a late goal at the Stadio San Paolo, although this time they were left with longer to respond and their hopes of snatching an equaliser would have been boosted by seeing five minutes of added time signalled.
However, those hopes were extinguished after two of the five minutes when Van Dijk put too much on his pass to Robertson and inadvertently sent Llorente through on goal, leaving the former Tottenham Hotspur man to fulfil his wish of exacting "revenge" on the Reds for defeat in the final last season.
It was Liverpool's first loss of the season inside normal time and also made it four successive defeats in away Champions League group games, although they will not panic just yet considering they overcame a similar setback last term to go on and lift the trophy.
Jurgen Klopp must now turn his attention to Sunday's Premier League showdown with Chelsea, who were also beaten in the Champions League tonight, whereas Napoli take on Lecce in Serie A this weekend.
NAPOLI (4-4-2): Meret; Di Lorenzo, Manolas, Koulibaly, Rui; Callejon, Allan (Elmas 75'), Ruiz, Insigne (Zielinski 66'); Mertens, Lozano (Llorente 69')
LIVERPOOL (4-3-3): Adrian; Alexander-Arnold, Matip, Van Dijk, Robertson; Henderson (Shaqiri 87'), Fabinho, Milner (Wijnaldum 66'); Salah, Firmino, Manebody check tags ::