Free-scoring Atalanta, last season's top-scorer with 98 goals, had netted 13 goals in winning its first three games but had no answer to Napoli's attacks in an extraordinary first half.
Mexican attacker Hirving Lozano notched a brace, Politano added a third, and Osimhen wrapped up the scoring for Napoli in the 43rd minute.
The former Lille striker chested down David Ospina's long ball upfield, turned and drilled low into the bottom corner for his first in three league games.
The Nigeria global controlled goalkeeper David Ospina's long ball before beating Marco Sportiello with his fine effort, which ultimately rendered Sam Lammers' second-half strike a mere consolation for Atalanta. The Argentine won possession, charged upfield and released Lammers, who clipped his shot past Ospina.
However, Serie A's disciplinary committee handed them a 3-0 defeat for failing to play a match against Juventus amid confusion over the COVID-19 rules and they also had a point deducted.
Down but not out, the visitors grabbed a consolation in the second half via the boot of Sam Lammers before Osimhen was replaced for the final seven minutes as Napoli moved up to third on the log with 8 points.
The goal would come as a welcome relief and boost of confidence for the young striker who had to settle for a lone assist in Napoli's last game where they outclassed Genoa in a 6-0 win.