The Florence club, eliminated from the Champions League at the last 16 stage by Bayern Munich in midweek, are 10th in the standings but have moved within five points of sixth spot and a guaranteed place in the Europa League qualifying round.
Seventh-placed Napoli, five behind Palermo in the fourth Champions League qualifying spot, took the lead early in the second half when injury-hit Argentine striker Ezequiel Lavezzi headed in his first goal at the San Paolo for a year.
Lavezzi then had a strong shout for a penalty turned down before Gilardino equalised 15 minutes after the break when he nodded home Stevan Jovetic's cross at the near post.
The Italy striker grabbed his second three minutes from the end when he flicked in Jovetic's header following a corner and Jovetic netted the third himself in stoppage time after Napoli goalkeeper Morgan De Sanctis had gone upfield to try to score.
Fiore coach Cesare Prandelli, whose side are in the Italian Cup semi-finals, has been linked in the media with Juventus or Italy for next season but he has hinted he would like to stay.
