Belgian forward Mertens scored from the penalty spot after Liverpool defender Andy Robertson was judged to have fouled Jose Callejon.
Jurgen Klopp’s side are the first winners of the competition to lose the opening game of the following campaign since AC Milan in 1994.
Goalkeeper Adrian had earlier made two keys saves for Liverpool, who initially struggled to impose themselves in the intimidating atmosphere of the San Paolo Stadium.
The 32-year-old, deputising for the injured Alisson, twice saved from compatriot Fabian Ruiz during the first period and produced an outstanding point-blank save from Mertens’ volley just after the break.
However, unlike the corresponding fixture last term, when Liverpool failed to register a shot on target in their 1-0 defeat, Klopp’s side did produce moments of slick football to threaten the hosts.
A flashing Mohamed Salah drive was superbly tipped to safety by Napoli goalkeeper Alex Meret, who also saved Sadio Mane’s toe-poked shot with the score at 0-0.
But while Klopp’s side have made a blistering start to the Premier League, averaging three goals per game, their failure to exploit several good breaks consigned them to a sixth defeat away from home in their last eight matches in the competition.
Liverpool’s failure to puncture the home defence was largely down to the impressive form of Kalidou Koulibaly, at the heart of the Napoli defence.
The Senegal international repeatedly demonstrated why he has been mentioned in dispatches as a target of the Premier League’s biggest clubs, throughout the summer.
Named the best defender in Serie A last term, the 28-year-old made several key interceptions and dispossessed both Roberto Firmino and Salah in one-versus-one situations.
And he continued in that vein, patrolling behind left-back Mario Rui to snuff out the danger posed by the Egyptian’s pace and trickery.
His reading of the game was exemplary throughout, ensuring he was rarely caught out of possession and was able to spring Napoli attacks.
