After a first half in which his side struggled to craft clear-cut chances at the Stadio Luigi Ferraris, captain and former Milan defender Luca Antonelli headed Genoa into the lead 13 minutes before the break.
Milan threw men forward after the break, but were unable to break through a resilient Genoa backline, with the hosts looking threatening on the break.
Ultimately Milan's fate was similar to that of champions Juventus, who also lost at the Stadio Luigi Ferraris, with Filippo Inzaghi's men beaten on the road in Serie A for the first time this season.
The triumph over an underwhelming Milan takes Genoa above Napoli into third after Rafael Benitez's side could only draw 2-2 at home to Empoli earlier on Sunday.
However, Rafael Benitez's men can take heart from the result having fought back from two goals down to salvage a point at the San Paolo.
Simone Verdi put the away side ahead in the 19th minute and they eventually doubled their advantage just after the break through Daniele Rugani, with Napoli seemingly staring at a first league defeat since September 21.
But the fight-back began with 23 minutes to go as Duvan Zapata headed in Dries Mertens' corner, before Jonathan de Guzman earned a point a few moments later, leaving Napoli fourth in the table.
ilan's city rivals Inter fared no better in the day’s late kick-off, though, as Andrea Stramaccioni returned to haunt his former employers in Udinese's 2-1 win.
Mauro Icardi had put Inter ahead in the closing stages of an otherwise unremarkable first half, but their lead did not last, with Bruno Fernandes' spectacular volley restoring parity with 30 minutes to go.
Cyril Thereau pounced on Rodrigo Palacio's ill-advised backpass to complete the turnaround 11 minutes later, as Roberto Mancini's Inter return continues to underwhelm.
Lazio remain in the hunt for a European place as they came from behind to beat rock-bottom Parma 2-1 away from home, while Atalanta produced a three-goal comeback to beat 19th-placed Cesena 3-2 in the day’s other clash.
