The visitors took the lead through penalty kick scorer Leandro Paredes, but Yacine Adli, Olivier Giroud, and Theo Hernandez scored to put the game away.
The outcome puts additional pressure on Mourinho as Roma drops to ninth position.
Because he was serving a touchline ban following two red cards in their previous two games, Mourinho was unable to attend the match from the sidelines.
Even though he was in the stands, he was still the target of boos when he made an appearance on the San Siro big screen.
It is widely believed that Mourinho, the former manager of Chelsea and Real Madrid, will depart the Italian city sometime between now and June, when his contract expires.