The Serie A side came out best in what was an even contest, with Mertens firing home after an Andy Robertson trip gifted the home side their big chance.
Substitute Fernando Llorente doubled the advantage in stoppage time at the end of the game, reacting fastest after a mix-up between Virgil van Dijk and Robertson to tuck the ball underneath Adrian and send the Naples crowd wild.
The first half was an open affair with plenty quality from both teams. It was Liverpool though that created the clearest scoring chances.
Sadio Mane saw a close range effort well saved by Alex Meret, while James Milner’s cross after a short corner was headed downward and just the wrong side of the upright by Roberto Firmino, with the Napoli goalkeeper stranded.
Mertens was a threat for Napoli at the other end, while home captain Lorenzo Insigne teed-up Mario Ruiz to force a low save from Adrian.
The stalemate was fair at the interval, though both sides would have felt they should have made a breakthrough in the opening exchanges of the second half.
Four minutes after the restart, Mario Rui’s cross found Mertens unmarked at the far post and his header seemed certain to break the deadlock, only for Adrian to push it over the crossbar with a superb one-handed stop.
On 55 minutes, Mane broke at pace with Liverpool forcing a two-on-one counter. The Senegal international’s pass was aimed at Mohamed Salah – who else – but it was poor and the chance was wasted.
Midway through the half a defensive mix-up between Kostas Manolas and Kalidou Koulibaly allowed Salah in, only for his first-time volley to be turned around the post by a fine save from Meret.
The game then appeared to be dawdling towards a stalemate but Napoli got their big chance with ten minutes remaining.
Jose Callejon cut inside Robertson and the full-back upended him with an outstretched leg. Adrian guessed right and got a glove on the resulting spot-kick, but Mertens had enough power on it to give his a lead.
The European champions rarely looked like restoring parity and their fate was sealed in the 91st minute when van Dijk inadvertently toe-poked the ball into the path of former Spurs frontman Llorente to score his first goal in Napoli colours.
The Reds now face a real struggle in Group E, with Salzburg impressing on matchday one as they fired six past Genk to take top spot in the table.