The 40-year-old Swede opened the scoring with a brilliant drill free-kick in the first half, scoring his 150th goal in the Italian top flight.
Frank Casey doubled the visitors’ lead from the penalty spot after Roma’s Roger Ibanez brought Ibrahimovic down the box.
The historic goal was another reminder of Ibrahimovic that he could still play at the highest level, having enjoyed success in Sweden, the Netherlands, France, England, Spain, Italy and the US.
Roma were given a glimmer of hope after Theo Hernandez was given a second yellow card with 25 minutes remaining, but the home side could only manage a 93rd-minute consolation goal through Stefan El Shaarawy.
The victory puts Milan level on points with Napoli – who beat Salernitana 1-0 – at the top of Serie A, with those two teams already a seven-point lead over Inter Milan in third.
The defeat is Roma’s first at home under Mourinho, but the club remains in a fourth and final Champions League qualifying place.
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