Napoli's relentless pressure finally paid off in the 88th minute when Raul Albiol drove a half-volley into the floor that bounced into the bottom corner.
Rafael Benitez's men should have equalised in the 25th minute when Jose Callejon's ball across the face of goal was inexplicably put wide by Gonzalo Higuain at the back post with the goal gaping.
Dries Mertens also went close when his effort from an acute angle struck the outside of the post.
The result means that Napoli remain third and 12 points behind leaders Juventus, while Chievo are just one point above the relegation zone in 16th.
