Duvan Zapata opened the scoring for the home side shortly before the hour mark, and Marek Hamsik made it 2-0 nine minutes later.
Mertens saw red for a poorly timed challenge almost immediately after Napoli's second, but Rafael Benitez's men held on to close in on faltering Roma, who have one win from their last seven league matches.
The match did not get off to the best of starts for Sassuolo, who saw defenders Luca Antei and Paolo Cannavaro - back at the club he represented for eight years until 2014 - forced off through injury in the opening 23 minutes.
Having dominated possession and chances in the first half, Napoli finally took the lead in the 61st minute, when Zapata stumbled his way through some questionable Sassuolo defending to convert a low effort.
The Belgian attacker had only been on the pitch five minutes when he was dismissed for a clumsy tackle from behind on Simone Missiroli.
