Defender Amir Rrahmani found the target six minutes into added time after Salernitana goalkeeper Guillermo Ochoa collided with a teammate.
Napoli moved up to sixth place, two points below the Champions League spots, with most of the teams ahead still to play this weekend.
Salernitana, who remained in last place, put up a fight at the Stadio Diego Maradona.
Antonio Candreva put Salernitana ahead with a long, curling shot into the top corner near the half-hour mark. It was Candreva’s sixth goal from outside the box since the start of last year - more than anyone in Europe’s five biggest leagues.
Matteo Politano equalised for Napoli with a penalty before the break after a foul on Giovanni Simeone.
Then Ochoa kept the visitors in the game until Rrahmani’s strike.
AAP
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