In a feisty encounter which was close to being called off due to crowd trouble, a pair of second-half strikes ensure Massimiliano Allegri's men return to San Siro with three points
Second-half goals from Zlatan Ibrahimovic and Antonio Nocerino in the also mean Alberto Malesani's men have now lost three of their last four league games, and will unsurprisingly pile the pressure on the former Bologna and Parma trainer.
The match was almost subject to premature abandonment just 12 minutes in, as tear gas was let off inside the Marassi, while disturbances outside the stadium threatened to boil over.
Fortunately for supporters, referee Domenico Celi was given the green light to resume proceedings several minutes later, although no clear goalscoring chances were to be carved out in the subsequent 30 minutes of action.
Despite Genoa starting more positively, the incident seemed to swing the game's momentum in the direction of Milan, who began with an early penalty shout after Antonio Nocerino was acrimoniously felled by Marco Rossi in the box.
Suddenly, against the run of play, Genoa almost stole the initiative from a shambolic piece of Rossoneri defending. Thiago Silva's wayward pass to Luca Antonini was read by Giandomenico Mesto in the box, but the flanker could only strike wide of Marco Amelia.
The second-half sprung into life as just nine minutes in, Kakha Kaladze conceded a penalty after picking up a second yellow and a consequent red for a clumsy challenge on Ibrahimovic, who got up to smash the spot-kick home.
It ought to have been 2-0 to the Scudetto holders a minute past the hour mark, but Robinho somehow ballooned over from a yard out with the goal at his mercy. Opposite number Marco Rossi also saw a chance from close range fall his way, but he could only manage to squeeze his effort wide.
And there was to be no surprise ending, as Milan promptly sealed the three points on 78 minutes, as Boateng drilled a low cross into the box, which was met by Nocerino, who continued his prolific start to the campaign by slamming the ball past Frey.
The defeat sees Genoa fall to 10th place in the Serie A table, but Allegri will be delighted to see his side take top spot and make it two wins and two clean sheets on the bounce.
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