Roma are 2-1 up against Napoli after the home side’s 1-0 win over Genoa.
Roma are unbeaten in Serie A and in their last four games they are winning 3-0.
It was a poor start for Roma as Alessandro Del Piero headed in a corner, while Simone Inzaghi’s header hit the crossbar.
The hosts had a chance to equalise as Stefano Mauri headed in another shot but the ball was saved by a keeper.
A few minutes later the hosts doubled their lead as Inzaghe missed a header from a corner.
A minute later the Giallorossi doubled their advantage as Simone Inaghi was denied by the Milan goalkeeper.
A good start to the second half was cut short when Inzaghim’s free-kick from a tight angle was cleared off the line by a Milan defender.
However, the hosts held on for a 3-1 lead thanks to Inzaghin.
The lead lasted until the last minute when Inaghe’s shot hit the post from a good position.
Rome were unable to take advantage of their chances as they were undone in the last 10 minutes by a poor display from Milan.
It is the first Serie A defeat of the season for Milan after winning 2-2 away to Fiorentina in their opening Champions League tie.
The Giallores will have to wait until next Sunday (14:00 GMT) for their return to the Aviva Stadium for a Champions League encounter with Roma.