Milan's win moves them level on points with league leaders Napoli.
Ibrahimovic, 40, opened the scoring with a free-kick and Franck Kessie converted from the spot after Roma's Roger Ibanez fouled the Swede.
Theo Hernandez was sent off for Milan, with Stephan El Shaarawy scoring in added time against his former club.
Earlier on Sunday, Napoli edged to a 1-0 win at struggling Salernitana and, like Milan, have won 10 of their first 11 games this term.
