Milan recorded their tenth win out of eleven league games this term to join Napoli at the top of the table on 31 points.
Ibrahimovic opened the scores with a free kick after 25 minutes and the Swede won a penalty in the second half which was converted by Franck Kessie before Stephan El Shaarawy halved the deficit for the hosts late on.
Stefano Pioli’s men held out for the win despite having Theo Hernandez sent off in the 66th minute.
Ibrahimovic’s strike was the 400th league goal of his career, and the 40-year-old who was part of the last Milan side to win the Serie A in the 2010/2011 season, is optimistic this current crop of players can go all the way this term.
"We'll try. We believe in this, we've done well so far, but it's a long season and we must continue to be consistent in our work," Ibrahimovic told DAZN after the game about their title aspirations.
"We believe, but it's early days. Take it one game at a time."
"It was a great performance, we played with a lot of confidence and our style," Ibrahimovic said after scoring his fourth direct free-kick in Serie A and first since January 2012.
"We knew it wasn't easy, Roma were unbeaten at home this season, but we played really well and must continue with this belief and tempo."
