Alessio Romagnoli's freak goal with the last kick of the game beat Genoa 2-1 on Wednesday and sent Milan into the Champions League places.
Both sides seemed to be heading for a share of the spoils, until Romagnoli hooked the ball over Ionut Radu right at the death to make up for his earlier own goal.
Lucas Biglia pulled up with a calf injury so Tiemoue Bakayoko partnered Franck Kessie and Hakan Calhanoglu in Milan’s midfield.
With Davide Calabria also out of the matchday squad, Gennaro Gattuso switched to a 3-5-2 formation as Ricardo Rodriguez played as a makeshift centre-back.
The Diavolo ended a two-match losing steak last weekend, beating Genoa’s city rivals Sampdoria 3-2, and they faced a Rossoblu side with two draws from two games under the returning Ivan Juric.
The visitors were spearheaded up top by Serie A top scorer Krzysztof Piatek, although the Pole had not scored since October 7.
The match was originally due to be played in Week 1 but was postponed after part of the Morandi bridge collapsed, killing 41 people.
Suso got Milan off to a flier in just the fifth minute, his rocket flying past Ionut Radu, although Piatek almost pulled one back for Genoa when he fizzed a volley into side-netting from close range.
Gianluigi Donnarumma was lucky not to get caught in possession towards the end of the first half, while Bakayoko didn’t cover himself in glory with a series of misplaced passes.
One of them resulted in the Rossoblu’s equaliser as Christian Kouame was gifted a shot at Donnarumma’s near post, which took a wicked deflection off Romagnoli before looping in.
Radu then pulled off a string of top saves to deny the likes of Gonzalo Higuain and Franck Kessie, but his punch in stoppage time fell straight to Romagnoli, who lobbed the Romanian with a hooked volley.
Milan 2-1 Genoa
Suso 4, Romagnoli 90 (M) Romagnoli og 56 (G)
Milan: G Donnarumma; Musacchio, Romagnoli, Rodriguez; Suso, Kessie, Bakayoko, Calhanoglu (Castillejo 83), Laxalt (Abate 63); Cutrone, Higuain
Genoa: Radu; Biraschi, Gunter Koray, Zukanovic; Lazovic, Romulo (Veloso 67), Mazzitelli (Omeonga 78), Bessa, Criscito; Kouame, Piatek (Pandev 85)