An involuntary assist from Roma midfielder Daniele De Rossi set up the decisive goal in the 20th minute as the visitors maintained their perfect start to the season.
The Roma captain accidentally set up Insigne when a loose ball fell at his feet on the edge of the box, sending the forward through with only the goalkeeper to beat.
The 26-year-old made no mistake with the opening, firing low beyond the keeper to score the 100th goal of his career.
Roma defender Kostas Manolas left the field with what appeared an injury in the second half which saw the visitors preserve their 100 per cent record, Napoli goalkeeper Pepe Reina blocking a header from Federico Fazio.
It was the first league match this season in which Napoli didn’t score at least three goals.
Still, after eight wins in their first eight matches the Partenopei remain on course for their first title since 1990, when Diego Maradona played.
Napoli visit Manchester City in the Champions League on Tuesday, while Roma visit Chelsea a day later.