Osimhen, the leading goal-scorer last season with 26, scored in each half to help Napoli get its title defence off to a good start on Saturday.
Frosinone took a surprise lead in the seventh minute through an Abdou Harroui penalty before Matteo Politano equalised.
It was a positive debut for new Napoli coach Rudi Garcia, who replaced Luciano Spalletti in the offseason. Spalletti left Napoli after steering the southern team to their first Serie A title in 33 years, before being appointed as Italy coach on Friday following Roberto Mancini’s shock resignation.
Frosinone also had a new coach in Eusebio Di Francesco after he took over from Fabio Grosso, who left the team after leading them to their first ever Serie B title.
And it was the home side who surprisingly scored the first goal of the new season after new Napoli signing Jens Cajuste clattered into the back of Jaime Baez. Harroui struck the resulting penalty into the bottom right corner.
It took Napoli until the 24th minute to get back on level terms when Politano’s scuffed shot bobbled out of the Frosinone goalkeeper’s grasp.
Napoli thought they had the lead 10 minutes later, but VAR ruled out Giacomo Raspadori’s strike for offside by Cajuste in the buildup.
Napoli went in front three minutes from halftime. Giovanni Di Lorenzo used his strength to hold off a defender and pulled the ball back for Osimhen who blasted into the roof of the net.
Osimhen almost scored a stunning goal seconds later but his effort curled just past the top of the right upright.
He sealed the result 11 minutes from time when he sprung the offside trap to run onto a Di Lorenzo through ball and fired it into the bottom right corner.
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AAP