Former Milan defender Manuel Locatelli scored the only goal of the game in the 63rd minute, after Rossoneri defender Malick Thiaw was sent off shortly before halftime.
Milan would have moved back to the top with a win and gone seven points clear of Juventus. Instead, the Bianconeri consolidated third place and cut the gap to one point.
They are two behind league leaders Inter, who won 3-0 at Torino on Saturday.
Both teams were missing a number of players through suspension and injury, including Juventus midfielder Nicolo Fagioli, who was banned for seven months earlier this week for his part in a betting scandal.
Milan started strongly, but their hopes of taking all three points diminished five minutes before halftime when Thiaw was shown a straight red card for hacking down Juventus forward Moise Kean.
The visitors still needed a stroke of luck to take the lead, Locatelli's effort taking a huge deflection off Milan midfielder Rade Krunic to leave goalkeeper Antonio Mirante completely wrongfooted.
Stephan El Shaarawy scored in the final minute as Roma snatched a confidence-boosting 1-0 win over Monza, who played more than half the match with 10 men.
Roma coach Jose Mourinho furiously celebrated the goal, which gave his team only their fourth league victory of the season, but was subsequently dismissed after making a 'crying eyes' gesture at Monza coach Raffaele Palladino.
Monza defender Danilo D'Ambrosio was somewhat harshly shown a second yellow card four minutes before halftime and sent off.
Filippo Inzaghi recorded a point in his first match back coaching in Serie A in two years as his Salernitana side snatched a 2-2 draw against Cagliari in what looked an early season relegation battle.
In a dramatic late flourish, Nicolas Viola appeared to have won it for Cagliari when he scored with two minutes remaining, barely two minutes after Boulaye Dia had canceled out Zito Luvumbo's 79th-minute opener.
But Salernitana were awarded a penalty deep into stoppage time, which Dia smashed home to level the scores.
The result maintained the status quo at the bottom of Serie A, with Salernitana a point above bottom club Cagliari.
Atalanta moved to within a point of the top four with a 2-0 win over promoted Genoa, while Bologna beat Frosinone 2-1.
13°C