AC Milan took the lead after 13 minutes when Theo Hernandez’s free-kick was deflected back off the wall and Pierre Kalulu headed the ball down to Rebic, who struck it powerfully into the right side of the net.
Against the run of play, the Grifone equalised in the 37th minute. Miha Zajc took the corner from the right, Destro easily escaped the attention of Fikayo Tomori, and he headed the ball into the net with considerable ease.
Rebic should have given the Rossoneri the lead again three minutes into the second half after some great play on the right between Kalulu and Alexis Saelemaekers but he blasted his shot over the bar.
Scamacca tried his luck from long range but his firm shot was lacking accuracy. AC Milan defender Simon Kjaer nearly scored as well but his header went wide.
The Rossoneri regained the lead after 68 minutes when Hakan Calhanoglu’s corner took a feint touch of Tomori and the ball was deflected into the net off the back of Scamacca. The Grifone youngster was taken off shortly after for Eldor Shomurodov.
Rebic tried to get his second goal with a volley from his right foot but Perin made a routine save.
Genoa nearly equalised in the 86th minute after AC Milan goalkeeper Gianluigi Donnarumma spilt a cross but Andrea Masiello had his shot blocked by Kjaer and Valon Behrami had the rebound blocked by Tomori.
AC Milan remain in second place in Serie A after 31 games and go up to 66 points while Genoa remain 14th with 32.