In the absence of the Nigeria forward, who has scored two Serie A goals this campaign, Gennaro Gattuso opted to have Dries Mertens lead Napoli's attack while Senegal centre-back Kalidou Koulibaly marshalled the defence.
Kessie and Bennacer produced fine performances in the middle of the park for AC Milan while the latter assisted Jens Hauge to seal all three points for the Rossoneri in stoppage time.
Zlatan Ibrahimovic opened the scoring at the Stadio San Paolo in the 20th minute, and he later made it 2-0 with his second goal of the night in the 54th minute.
A few minutes after the hour-mark, Mertens reduced the deficit for Napoli but it was not enough to inspire a comeback as they suffered their second straight loss at home.
Bennacer completed the most tackles in the encounter (five) while Kessie managed the best pass accuracy (94.1 per cent) and they were both in action for 90 minutes.
Sunday's triumph stretched AC Milan's dominance at the summit of the Serie A table to 20 points after eight matches as Napoli dropped to sixth with 14 points.
Gattuso will hope to have Osimhen ready for Thursday's Uefa Europa League clash against Rijeka at home, after he missed their last match due to a red card he picked up against Real Sociedad on October 29.