It took the hosts just three minutes to open the scoring, with Higuain gaining possession inside the box and making no mistake with his reliable right foot.
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Napoli came within inches of doubling their lead following a swift break in the 12th minute - a move that ended with Callejon crashing an effort against the visitors' crossbar.
The post came to the visitors' rescue moments before the break as Higuain picked out Marek Hamsik in the box and the Slovak rattled the upright.
Alessandro Florenzi was lively for Roma in the second period, and he almost levelled the game just before the hour mark as Rafael produced a good stop to prevent his effort from finding the bottom corner.
But Napoli deserved their slender lead and continued to push for a second until the end, coming close in the 74th minute when Dries Mertens right-footed effort from the edge of the box was smothered by Roma goalkeeper Morgan De Sanctis.
They made the result safe five minutes from time as Higuain found Callejon in the area, allowing the Spaniard to bury the finish, and Roma in the process.