The visitors had looked on course for a hard-fought point despite a laboured performance severely lacking the intensity usually seen from Jurgen Klopp's side, but Lorenzo Insigne snatched the victory for Napoli with a winner in the final minute of normal time.
It was a deserved win for the home side, and one which blows Group C wide open with Napoli moving top on four points, one ahead of Paris Saint-Germain and Liverpool on three apiece.
Klopp made just one change from the team which drew with Chelsea at the weekend as Naby Keita replaced Jordan Henderson in the starting lineup, but the returning Guinean - making his Champions League debut for the club - endured a short and unsuccessful spell on the field.
It was his misplaced pass which gifted Napoli the best chance of the half after just 11 minutes, but Insigne could not take full advantage as he sent a low effort bobbling narrowly past the far post.
Insigne threatened again five minutes later when he curled a long-range effort high and wide of the target, and there was more cause for concern for Liverpool shortly afterwards as Keita went down innocuously off the ball clutching his back.
The summer signing ended up needing to be stretchered off, and his replacement Henderson quickly set about trying to inject some energy and enthusiasm into Liverpool's lacklustre start.
It was proving to be an arduous night for both sides, though, and Liverpool's best attacking moment of the opening 45 minutes saw Georginio Wijnaldum drag a tame effort comfortably wide from range shortly before the half-hour mark.
The Reds reached half time without registering a shot on target for only the second time this calendar year, but there was a bit of work for Alisson Becker to do when he collected an Arkadiusz Milik effort on the turn at the second attempt.
Klopp's side offered minimal attacking threat in the second half either, but Napoli did begin to up the tempo and Alisson was forced into two saves in quick succession shortly after the restart when he denied long-range strikes from Milik and then Fabian Ruiz.
The final product was just missing for the hosts at various stages throughout the match, and Ruiz took too long over another presentable opportunity before Milik fired well wide with a first-time effort from the edge of the box.
It was Napoli who continued looked the most like scoring, though, and Liverpool's best moment of the second half saw Mohamed Salah curl his effort wide after the ball had only been cleared as far as the Egyptian 20 yards from goal.
The Reds failed to truly test David Ospina in the Napoli goal at all, and it became increasingly evident that they were hanging on for a point when Napoli's pressure began to grow in the final 15 minutes, with Joe Gomez needed to clear a well-controlled Jose Callejon volley off the line.
The hosts came even closer to breaking the deadlock eight minutes from time when Mario Rui's dangerous ball in from the left was met by substitute Dries Mertens, only for his close-range volley to come crashing back off the crossbar with Alisson well beaten.
It looked as though Liverpool would hold out for a valuable away point which would have kept them top of Group C, but Napoli finally struck with just 30 seconds remaining of normal time as Insigne applied a simple finish from close range after Alisson had been taken out of the game by Callejon's cross.
There was no time for Liverpool to respond as their winless run extended to three games - having won their opening seven matches across all competitions - while Napoli register their first ever win over the five-time champions of Europe at the third attempt.
Liverpool will now look to bounce back in their mouth-watering top-of-the-table clash with Manchester City at Anfield on Sunday, while Napoli host Sassuolo this weekend.
NAPOLI (4-3-3): Ospina; Maksimovic, Albiol, Koulibaly, Rui; Callejon, Allan, Hamsik (Zielinski 81'), Ruiz (Verdi 68'); Milik (Mertens 68'), Insigne
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold, Gomez, Van Dijk, Robertson; Milner (Fabinho 76'), Wijnaldum, Keita (Henderson 19'); Salah, Firmino, Mane (Sturridge 89')