Milan had the first chance of the game after just seven minutes. After Leo Ostigard had denied Youssouf Fofana with a superb last-ditch tackle, Matteo Gabbia met the resulting corner with a thumping header that crashed off the face of the crossbar.
However, this was not the beginning of a Milan onslaught as Genoa settled into the game.
It was one of their own that did the damage for the hosts as Lorenzo Colombo showed his parent club what they are missing just before the half-hour mark. He got free of the clutches of Gabbia and diverted Ruslan Malinovskyi’s pass past Mike Maignan to open the scoring.
Massimiliano Allegri’s side had a golden chance to equalise 10 minutes before the break but they spurned it. After Nicola Leali made a superb close-range stop from Leao, Fofana had the goal at his mercy but slipped at the worst possible time and missed the ball completely, meaning Daniele De Rossi’s charges led at the break.
The Rossoneri came out after the break piling the pressure on the visitors and thought they had an equaliser on 57 minutes when another Gabbia header appeared to have glanced in off the post. However, replays showed that Christian Pulisic had thrown himself at the ball at the back post and diverted it in via his arm, and VAR correctly ruled it out.
Another chance went begging less than 10 minutes later when Davide Bartesaghi slid his effort across the face of goal having been picked out by half-time sub Ruben Loftus-Cheek.
Leali made another couple of good saves as Milan kept up the pressure, first from Pulisic’s glancing header before he held Zachary Athekame’s low, hard shot from range.
Milan continued to probe right to the end and Liali made perhaps his best save of the night on 87 minutes when he produced a flying stop to deny Pulisic on the volley at the back post.
There was a drama-filled stoppage time at the San Siro as it looked as though the hosts had rescued a point when Leao nodded home Niclas Fullkrug’s flick on from a corner.
But then, deep into time added on, Bartesaghi sent Mikael Egill Ellertsson tumbling in the box with the spot kick confirmed by VAR. However, the delay perhaps got into the head of taker Nicolae Stanciu, who blazed his effort over the bar and left the game honours even.
Flashscore Man of the Match: Nicola Leali (Genoa)