The Reds, who lost Naby Keita inside the opening 20 minutes, were required to withstand pressure from the hosts throughout the contest.
Napoli twice went close to breaking the deadlock in the final stages, but Joe Gomez first denied Jose Callejon’s well-struck effort on the line before substitute Dries Mertens rattled the crossbar from inside the six-yard box.
However, with the game looking like it was heading for stalemate, the Italians finally breached the visiting defence when Insigne slid in Callejon’s low centre at the conclusion.
It means after two games played, Napoli top Group C with four points, and Liverpool and Paris Saint-Germain are both one behind on three.
The team news…
Jürgen Klopp’s teamsheet showed just one change to the line-up from Saturday’s draw at Chelsea as Keita returned in place of Jordan Henderson.
The first half…
Liverpool kicked off in the Stadio San Paolo aiming to enhance their chances of progression from Group C into the knockout stages of the competition, having dramatically defeated Paris Saint-Germain 3-2 on matchday one.
Napoli, however, were eager to build upon a point earned at Red Star Belgrade, and – roared on by their vocal supporters – had the game’s first chance with 11 minutes on the clock.
Keita conceded possession inside the visitors’ half and the ball was eventually worked to the unmarked Insigne on the left corner of the Reds’ box, though the forward could only angle a low drive wide of the far post.
Then, shortly after, Liverpool were dealt a blow as Keita went to ground seemingly unchallenged and was carried from the field, meaning an early introduction into the action for Henderson.
By this point, the hosts had begun to settle and were gradually increasing the pressure on the away team’s back line; just after the half-hour, Arkadiusz Milik’s spin and snap-shot brought a save out of Alisson Becker.
Nevertheless, the interval arrived without an indent on the scoresheet.
The second half…
Napoli fashioned the first opening of the second period shortly after the re-start when Milik’s blast from 20 yards was parried by Alisson, before the stopper thwarted an effort from Fabian Ruiz soon after.
Next, a last-ditch challenge from Trent Alexander-Arnold was required to prevent Milik getting a clear shot at goal as the home team cranked up the pressure.
At the other end, a half-cleared corner presented an opportunity to Mohamed Salah just outside the area; however, his swipe back towards goal was off target.
Back came Napoli and Liverpool had Gomez to thank for keeping the scoreline level when he blocked Callejon’s crisp first-time volley on the line with 15 minutes remaining.
Fabinho entered the action in place of James Milner shortly after, but Gli Azzurri went even closer to taking the lead when Mertens cracked the crossbar from yards out with a close-range strike.
With the conclusion edging ever nearer, Sadio Mane almost sent Salah through, but David Ospina raced from his line to clear.
However, Napoli got the goal they’d long been threatening in the last minute of normal time when Insigne arrived to nudge Callejon’s delivery over the line and secure three points for Carlo Ancelotti’s men.
The stats...
The table...