Osimhen opened the scoring for Napoli in the 24th minute, getting a last-minute touch to a goal-bound effort by Lorenzo Insigne.
The Nigerian striker was impressive again for The Blues, running the channels well and being a threat all through.
Amir Brahmani, Kalidou Koulibaly and Hirving Lozano were the other scorers for Napoli at the Stadio Friuli.
The 22-year-old has two goals this season in all competitions for Napoli.
He scored 10 last season, which only came in the Serie A.