They went past AS Roma and Lazio onto 34 points from 20 games while Genoa are 14th with 20.
Gattuso himself was suspended for insulting the referee after Milan's Super Cup defeat to Juventus on Wednesday. Genoa took the initiative and were kept out by three excellent Gianluigi Donnarumma saves in the first half. The 19-year-old goalkeeper frustrated the hosts again after halftime with a superb double save to deny Miguel Veloso and Daniel Bessa. Borini put Milan ahead, tapping in from Andrea Conti's low cross, in the 72nd minute and Suso finished off a counter-attack to add the second seven minutes from time. In between, Donnarumma turned Veloso's powerful shot onto the underside of the bar.
(Reporting by Brian Homewood; Editing by Ian Chadband)
