Ruben Amorim's men made a strong start to the encounter, scoring twice inside the opening 20 minutes to put themselves in control of the contest.
Genoa threatened early, with Milos Osmajić narrowly missing the target in the opening minute. However, Milan gradually took control and found the breakthrough in the 13th minute.
Alphadjo Cissé opened the scoring after Adrien Rabiot won possession and supplied the assist, allowing the young forward to finish from a central position.
The visitors doubled their advantage six minutes later. Gonçalo Ramos provided the pass for Christian Pulisic, who calmly finished to make it 2-0.
Genoa attempted to respond before the interval, but Milan goalkeeper Mike Maignan produced important saves to preserve his side's two-goal advantage.
The hosts increased their attacking pressure after the restart, searching for a way back into the match. Maignan continued to frustrate Genoa, making another important intervention to deny Vitinha in the second half.
Genoa eventually pulled one back in the 88th minute when Mikael Egill Ellertsson produced an impressive long-range finish to reduce the deficit.
The late goal set up a tense finish, but Milan held on through the closing minutes and stoppage time to secure all three points.
The victory takes AC Milan to 24 points from 11 matches, strengthening their position in the race for European qualification, while Genoa remain on 13 points.
Milan will return to Serie A action on 22 November when they welcome Frosinone to San Siro.
Full-time: Genoa 1-2 AC Milan
Goalscorers:
• AC Milan: Alphadjo Cissé 13', Christian Pulisic 19'.
• Genoa: Mikael Egill Ellertsson 88'.
Competition: Italian Serie A, Matchday 11.
Stadium: Stadio Luigi Ferraris.