The 33-year-old Belgian striker curled in a free kick and nodded in a simple finish to put his side two goals in front after 34 minutes, and the hosts could not muster a response.
Mertens is only the third Napoli player to reach 100 goals in Serie A, after Marek Hamsik (100) and Antonio Vojak (102).
Lorenzo Pellegrini's shot rattled the post for Roma in the second half but it was another disappointing big-game performance by Paulo Fonseca's side, who have not won any of their matches against fellow top-seven sides this season.
"We don't have the mentality to fight against these teams," Fonseca told Sky Italia.
"What I saw today was a team without courage, without mentality, which was then totally different in the second half.
"We wanted to play after the break and it was a different game. In the first half we were non-existent, we lacked bravery. When you're afraid of losing and playing, it's too difficult."