Evergreen striker Ibrahimovic made it 10 goals in six top-flight matches this season when his brace inspired a 3-1 win at Napoli, although he limped off with a hamstring complaint in the closing stages.
Yet Stefano Pioli's side marched on without their talisman against struggling Fiorentina, with Franck Kessie netting one first-half penalty and missing a second after Alessio Romagnoli opened the scoring.
Fiorentina undid an encouraging start in the 17th minute when Milan captain Romagnoli was left unmarked at the back post to nod in Kessie's flick-on from Hakan Calhanoglu's right-wing corner.
Dusan Vlahovic thumped against Gianluigi Donnarumma's near post as Cesare Prandelli's men searched for an equaliser but they were left with a mountain to climb when German Pezzella clumsily brought down Alexis Saelemaekers in the area.
Kessie coolly sent Bartlomiej Dragowski the wrong way but the Fiorentina goalkeeper levelled their personal battle in the 40th minute – springing to his left to keep out a poorly struck spot-kick after Martin Caceres bundled into the marauding Theo Hernandez.
Calhanoglu fizzed a fabulous half-volley into the side netting before half-time and came even closer in the 53rd minute, hitting the base of the left post.
Franck Ribery almost reduced the arrears two minutes later but Donnarumma was equal to the veteran campaigner's dinked effort – a squandered chance which summed up a Fiorentina display littered with moments of self-sabotage.
What it means: San Siro big hitters going blow for blow
You have to go back to the 2010-11 season, the final campaign before Juventus' ongoing dominance began, for the last time the Milanese clubs finished first and second in Serie A. Milan, inspired by Ibrahimovic's goals, prevailed on that occasion. His supporting cast look in fine order a decade on.
Milan remain the only team alongside Atletico Madrid in Europe's top five leagues to be unbeaten since the coronavirus shutdown and scored for a 29th consecutive game – equalling their previous best run in Serie A set between 1972 and 1973.
Calhanoglu shows his class
The Turkey playmaker did everything but get on the scoresheet, although his five shots (including one blocked) showed it was not for want of trying. Calhanoglu was Milan's creative inspiration throughout, making five key passes, completing 83.3 per cent of his passes in the opposition half and four of seven crosses.
The Fiorentina captain's attempts to lead by example backfired horribly when he conceded the crucial first penalty. Pezzella – an Argentina international – won only four of his nine duels during the contest.
Key Opta Facts
– Milan have picked up 23 points in the first nine games played in Serie A 2020-21 – their record at this point of the season in the three points per win era.
– Fiorentina have earned eight points in the first nine games played in Serie A this season. It is their worst tally at this point of a campaign since the introduction of three points per win.
– The Rossoneri have scored two or more goals for 11 consecutive Serie A games, equalling their record in the competition established between 1958 and 1959.
– Only Leicester City (eight) have taken more penalties than Milan (seven) in the top-five European Leagues.
– Romagnoli has scored three headers in Serie A for Milan. Only Ibrahimovic (six) has netted more among the Rossoneri.
– Kessie is one of three players born from 1996 onwards to have reached 25 Serie A goals, after Lautaro Martínez and Federico Chiesa.