Osimhen was among the scorers in a thumping win for Napoli, who have had a tricky summer after losing stalwarts Kalidou Koulibaly, Lorenzo Insigne and Dries Mertens. However Luciano Spalletti's team were on top form at the Stadio Bentegodi, with goals from their Nigerian forward, Khvicha Kvaratskhelia, Piotr Zielinski, Stanislav Lobotka and Matteo Politano ensuring they got off to a perfect start.
Verona battled and were level early in the second half through Kevin Lasagna and Thomas Henry, but shorn of last season's stars Giovanni Simeone - on his way to Napoli on loan - and Gianluca Caprari, there was little Gabriele Cioffi's side could do under a second-half onslaught. Napoli were on top from the first minute but were hit with a sucker punch just before the half-hour mark when, after Alex Meret tipped over Martin Hongla's shot, Lasagana tapped home Koray Gunter's flick-on of the subsequent corner.
But Napoli were deservedly level eight minutes later through new boy Kvaratskhelia, who marked an impressive debut by meeting Hirving Lozano's cross with a perfect header past Lorenzo Montipo. And in first-half stoppage time Osimhen put Napoli ahead with a carbon copy of Lasagna's opener from a corner, stretching to jab home Giovanni Di Lorenzo's knockdown.
An 'AFP' reporter at the game heard a section of the home support launch monkey chants at Osimhen, the latest episode of racist chanting at Verona who have a long history of far-right sympathies among their hardcore support. After netting his first goal of the season, Nigeria striker Osimhen took off his protective face mask and mimicked crying into a pitch-side camera, suggesting he had heard abuse before his goal.
Napoli's advantage only lasted two minutes after the half-time break as another debutant in Henry headed in his first Verona goal since arriving from local rivals Venezia. The Frenchman then accidentally gave Lasagna a bloody nose in the celebrations and a match which had almost everything then swung again in Napoli's favour in the 55th minute.
Classy Kvaratskhelia slid through Zielinski with a neat first-time pass and the Pole rolled home a calm finish which ended Verona's resistance. Ten minutes later the result was put beyond doubt thanks to a well-worked goal from Lobotka, who drove towards the hosts' goal unchallenged before simply passing the ball past Montipo.
And substitute Politano put the cherry on the cake with 11 minutes remaining after another flowing passing move ended with the Italian collecting Osimhen's lay-off and firing home low with his left home. Juventus complete the first round of fixtures later on Monday when they host Sassuolo in Turin.