Leading 1-0 from the first leg, Napoli’s advantage was quickly wiped out when Christian Eriksen scored direct from a corner.
Belgium forward Mertens made it 2-1 on aggregate after an assist from Lorenzo Insigne following a counter-attack. It was his 122nd goal for Napoli, one more than Slovakia’s Marek Hamsik.
Mertens, who is nicknamed ‘Ciro’ by Napoli fans to reflect his longstanding relationship with the club and city of Naples, is now seven goals clear of club legend Diego Maradona,
Napoli, who last won the competition in 2014, will meet Juventus in the Coppa Italia final without any fans present on Wednesday at the Stadio Olimpico in Rome.
Fabian Ruiz’s goal had given Napoli a semi-final first-leg lead in front of almost 60,000 fans in Milan on 12 February.
There were no supporters present as Napoli finished off the job – despite conceding after two minutes.
The visitors were level on aggregate when former Tottenham midfielder Eriksen bent a corner straight into the back of the net, eluding keeper David Ospina.
Inter twice went close to extending their advantage but former Arsenal keeper Ospina, who was excellent after his error for the opener, produced fine saves to deny Romelu Lukaku and then Antonio Candreva.
Shortly before half-time Mertens made club history and handed back control to Napoli after the former PSV Eindhoven player’s composed finish from Ospina’s long clearance.
Insigne went close to winning it on the night for Napoli but sent his shot just wide of the post before Ospina made a superb late save to keep out Eriksen and substitute Victor Moses put the follow-up over the bar.
Antonio Conte insists Inter deserved to reach the Coppa Italia Final more than Napoli over two legs.
‘Their goalkeeper was Man of the Match and we dominated.’
“Over the two legs, I believe we deserved to reach the Final. I have very little to reproach my lads for after this evening, because this is the aggressive football I want to see, trying to dominate the game.
“We created many chances and perhaps could’ve been more clinical in front of goal, but David Ospina made some stunning saves and was decisive.
“It’s disappointing to concede that goal, as it was a naïve error we could’ve avoided. If we want to fight it out with a team like Napoli, we created so much, dominated the match and this performance bodes well for the future.
“On the Napoli goal, it was a corner and we had the right positions, but then there was a ricochet and we lost our shape. It was an error, we weren’t focused enough at that moment and we paid a heavy price. At least it’ll show us that these details are the difference at this level and help us to grow.”