Instead, the guests won the top match 1-0.
Zlatan Ibrahimovic played the whole match for Milan but had to leave the pitch goalless.
It also got the rest of the team after a controversial VAR situation in the final minutes.
Milan pressed for an equalizer in the last regular minute.
And after a number of pinballs in the penalty area, the ball reached Franck Kessie who scored 1-1.
Offside situation
Then the VAR room alerted the referee to a possible offside situation.
The pictures showed that Olivier Giroud was in offside position, but that he did not touch the ball that was shot at him.
Instead, a Napoli defender got his toe on the ball.
But the referee ruled that the Frenchman still influenced the game.
The goal was therefore ruled out - and Milan lost the match.
Napoli's winning goal came in the fifth minute when Elif Elmas stayed in front of a corner and nodded in 1-0 to the guests.
The result means that Napoli steps past Milan in the table and takes over second place.
Inter leads by a margin of four points.