The former Chelsea forward set up Alexis Saelemaekers’ third-minute opener with a driving run down the left before doubling Milan’s lead in the 31st.
However, Napoli were given hope when Milan left-back Pervis Estupinan was sent off for pulling back Giovanni di Lorenzo with the right-back ready to tap into an empty net.
The ex-Brighton man was originally shown a yellow card before a video assistant referee review upgraded it to a red.
Kevin se Bruyne converted the penalty to halve the deficit but, despite their man advantage, Antonio Conte’s side were unable to force an equaliser.
Victory takes Massimiliano Allegri’s side above Napoli, who suffered their first league loss of the season, on goal difference.
Roma are also level with the top two on 12 points from five games after goals from strikers Artem Dovbyk and Matias Soule took them to a 2-0 win over Hellas Verona.
