Genoa 1 Milan 0: Skipper Antonelli seals points
Gian Piero Gasperini's side have not lost in the league since September as they bounced back from their surprise Coppa Italia exit at the hands of Empoli in midweek.
The win over a lacklustre Milan side - without suspended midfielder Michael Essien - takes Genoa above Napoli into third after Rafael Benitez's side could only draw 2-2 at home to Empoli earlier on Sunday.
After a first half in which his side struggled to fashion clear-cut opportunities at the Stadio Luigi Ferraris, captain and former Milan defender Luca Antonelli gave Genoa the lead from a corner 13 minutes before the break.
Milan huffed and puffed after the interval, but were unable to break down a disciplined Genoa defence, with the hosts looking more than capable on the break.
Ultimately Milan befell the same fate as champions Juventus in losing at the Stadio Luigi Ferraris, as Filippo Inzaghi's men were beaten on the road in Serie A for the first time this season.
Jeremy Menez had Milan's first effort on goal as he cut in from the left and tested Mattia Perin after 11 minutes as the game started in a fairly tentative manner.
Stephan El Shaarawy - featuring against his former club - saw a header on goal easily gathered by Perin midway through the half, before Genoa started to dominate possession.
Gasperini's men kept the ball well and moved Milan around without getting behind them, but it was the visitors who continued to have the better of the chances.
Menez fired a one-on-one straight at Perin before the half-hour mark after robbing Juraj Kucka of the ball in midfield before Genoa took the lead.
Having failed to make the most of their many corners, Genoa eventually made Milan pay at the ninth attempt as Antonelli's glanced header beat Diego Lopez to the goalkeeper's left.
Diego Perotti almost made it two before the interval but his strike was blocked on the goal-line by Daniele Bonera.
Milan continued to struggle to create opportunities after the interval and Keisuke Honda fired a disappointing free-kick into the wall.
Giampaolo Pazzini was introduced late on for Honda to try and inject some impetus but to no avail, with Inzaghi perhaps wishing he could call on in-form striker Alessandro Matri - the Milan forward who was lining up against his parent club.
Giacomo Bonaventura could have salvaged a point late on when the ball fell kindly for him inside the penalty area, but the midfielder could only scoop the ball over the crossbar.
Inzaghi will now need to focus Milan's attention on tricky upcoming encounters with Napoli and Roma before the year's end, while Genoa look almost certain to end 2014 in a European place after another impressive win.