Osimhen may have doubled the guests’ lead within the 61st minute however his effort was dominated out for a foul on Spezia defender Mattia Caldara.
The Nigerian netted seven minutes later, nonetheless, with a close-range header following a mistake by Spezia defender Ethan Ampadu.
One other error by the Spezia defence gifted Osimhen the prospect to make it 3-0 within the 73rd minute along with his sixteenth league aim of the season, a private file.
Napoli provisionally elevated their benefit over second-placed Inter Milan to 16 factors. Spezia remained seventeenth, hovering 5 factors above the relegation zone.