Mertens was set up for the opening goal by Marek Hamsik with a clever through ball but still needed to beat the offside trap and two defenders before chipping cleverly over Roma goalkeeper Wojciech Szczesny in the 25th minute.
The Belgian international added a second five minutes into the second half, touching in a cross from the left by Lorenzo Insigne.
But Napoli had to survive an anxious final five minutes after Kevin Strootman pulled a goal back in the 89th minute and Mohamed Salah, who had hit the upright, and Diego Perotti came close to a stoppage-time equaliser with Napoli's Pepe Reina pulling off a dramatic save to ensure the points.
Napoli are now back in contention for an automatic Champions League berth next season as they moved on to 57 points. Second- placed Roma have 59, seven behind leaders Juventus who play at Udinese on Sunday.
(Reporting by Mark Gleeson; Editing by Ed Osmond)
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