Genoa secured their first win under Andriy Shevchenko against Salernitana in the Coppa Italia and have booked a place in the last 16 against Milan.
The Grifone had to wait until the 76th minute before Caleb Ekuban scored from a header, as Yayah Kallon found the striker with a cross from the left.
It was a game of few chances at Marassi, but Stefano Colantuono’s men went home empty handed after the one goal that separated the sides on Tuesday.
Shevchenko, who replaced Davide Ballardini at the helm, has thus secured his first win and is now hoping to build on the success in the league when the Grifone travel to Lazio in Serie A this weekend.
Milan await Genoa in the last 16 of the Coppa Italia, while Udinese and Venezia had already secured a place in the next round with their respective wins against Crotone and Ternana earlier on Tuesday.