Moscardelli, on as a 59th-minute replacement for Cyril Thereau, fired home from close range in the 72nd minute after Ignacio Fideleff had booted an attempted clearance into his path.
The home side, smarting from Sunday's defeat at Parma, started strongly and fashioned their first shot in the third minute when Rinaldo Cruzado's effort was saved by Morgan De Sanctis.
The visitors came close in the ninth minute when Blerim Dzemaili shot wide, and two minutes later the same player tried a shot from distance which sailed over the crossbar.
Napoli continued to hold the upper hand with Mario Santana coming close on the end of a swift counter-attack then Camilo Zuniga shot inches over the crossbar from long range.
Goran Pandev shot wide, then with half-time approaching the Macedonian was inches from connecting with Santana's cross from the left in front of goal.
Chievo looked brighter at the start of the second half with Perparim Hetemaj bringing a stretching save out of De Sanctis before the introduction of Moscardelli made a big difference.
The striker forced another save out of De Sanctis from long range and moments later the Napoli keeper was in action again with a fine dive to deny Alberto Paloschi.
A Chievo goal looked like coming and it finally arrived through Moscardelli, who could have made it 2-0 10 minutes from time when he hit a left-foot shot which was well saved by the busy De Sanctis.