Osimhen had a goal ruled out for offside in the first half, but Napoli went into the break with a 1-0 lead.
Captain Giovanni Di Lorenzo put the hosts ahead late in the first half.
Andre-Frank Zambo Anguissa combined with Mario Rui to pull back from the by-line, as Di Lorenzo took a touch and smashed the finish off the underside of the crossbar.
Osimhen added the second three minutes after the break.
The Nigeria international has now scored 13 goals in 15 league appearances for the Partenopei this season.