Palermo goalkeeper Salvatore Sirigu made a series of splendid saves before Edinson Cavani beat the Sicilian club's offside trap in the fifth minute of added time and crossed to Maggio in front of an empty net.
Before the goal, Sirigu blocked shots from Ezequiel Lavezzi, Cavani and Maggio at the San Paolo stadium.
“We should have scored five goals,” said Napoli coach Walter Mazzari. “It would have been a shame not to win.” The victory moved Napoli level with Juventus on 27 points, six behind leader AC Milan.
Palermo remained tied with Inter Milan, Sampdoria and AS Roma with 23 points each.
Argentina forward Javier Pastore had one of Palermo's best chances in the 60th, with his shot from beyond the area blocked by Napoli goalkeeper Morgan De Sanctis.
The match may have marked the last Serie A fixture before a players' strike called for next weekend.
In Spain, Nouioui Lassad's second-half goal saw a defensive Deportivo La Coruna squeak out a 1-0 victory over Hercules in Spain on Monday.
Neither club created many clearcut chances at El Riazor stadium, but the Galicians finally broke through in the 73rd-minute through striker Lassad. Hercules rarely even tested the Deportivo goal.
Deportivo improved to 17 points while Hercules stayed on 15 points.
Barcelona leads the league table with 37 points after 14 rounds - two better than Real Madrid. Villarreal is third with 30.
