Manolo Gabbiadini blasted against the crossbar as the visitors almost grabbed a quick equaliser, only for Mertens to make the game safe by curling in a 25-metre free kick in the 62nd minute.
The win gave third-placed Napoli 39 points from 18 games, two behind Roma who lost 3-0 at leaders Juventus on Sunday.
In their previous six games, Rafael Benitez's Napoli had lost 3-0 to Juve and 1-0 at home to Parma, beaten Lazio and Inter Milan and dropped points at home to Udinese in a 3-3 draw and in a 1-1 draw at Cagliari.
It was sixth from bottom Sampdoria's first defeat in six games since Sinisa Mihajlovic took over as coach.
(Reporting by Brian Homewood, editing by Tony Jimenez)
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