Giampaolo Pazzini scored the opener only to be then forced off through injury, but his replacement, Mario Balotelli, added a second before Kevin Constant saw red
The Rossoneri were nowhere near their best at the Luigi Ferraris, breaking the deadlock against the run of play through Giampaolo Pazzini 22 minutes in.
Massimiliano Allegri's men then survived three strong penalty appeals before bagging a crucial second goal through the returning Mario Balotelli on the hour mark. Kevin Constant saw red for violent conduct soon after but Milan held on to move to within two points of second-placed Napoli.
The resurgent Rossoneri went into the game on the back of a rousing victory over Lazio that had propelled them into third in the Serie A standings. However, they made a subdued start at the Luigi Ferraris, with Genoa looking the more likely scorer during a cagey opening quarter.
However, the visitors suddenly sparked into life midway through the first half when M'baye Niang unleashed a terrific curling effort from the right-hand side of the area that Sebastien Frey acrobatically pushed away to safety. Just two minutes later, Milan was ahead, Pazzini crashing home a wonderful drive from the edge of the area via the underside of the crossbar.
It was a terrific strike made all the more remarkable by the fact that Pazzini had, just moments beforehand, suffered an ankle injury that would force him from the field immediately after his goal. Indeed, the former Sampdoria striker had only been positioned on the edge of the box because he was struggling so badly to keep up with an attack that he himself had instigated.
Pazzini's withdrawal resulted in an early introduction for the fit-again Balotelli, who announced his return with a needless push on Juan Manuel Vargas that earned the volatile striker a booking.
If that foul irked the home fans, they were positively livid when referee Antonio Damato waved away three penalty appeals in the space of 10 minutes. In the first instance, it was highly debatable whether Cristian Zapata, who had his arms by his side, intended to handle a ball that came at him rapidly via a deflection. However, in the second instance, Niang had blatantly blocked an attempted header back across goal from Borriello with an outstretched arm.
Niang was at it again just over five minutes before the break when he blatantly pushed Andreas Granqvist as the Swede was attempting to connect with a free kick from the left wing. Once again, though, Damato was inexplicably having none of it. Consequently, Genoa went into the half-time interval feeling extremely hard done by.
Genoa's sense of frustration was only exacerbated five minutes into the second half when Cesare Bovo struck Abbiati's left post with the most sweetly struck free kick from all of 35 yards. Balotelli threatened for the first time moments later, with a shot that flew just over, but Genoa was still bossing proceedings and it responded with a Borriello snapshot that was easily dealt with by Abbiati.
However, the previously anonymous Mathieu Flamini suddenly came to the fore for Milan, driving into the area before needlessly trying to win a penalty with an obvious dive, before then redeeming himself somewhat by drawing a stunning fingertip save out of Frey after another awesome surge from midfield. Indeed, from the resulting corner, Milan claimed the killer second goal, Zapata deftly flicking a half-clearance into the path of Balotelli, who was calmness personified as he whipped the ball past Frey into the bottom left corner of the Genoa goal.
Just seven minutes after effectively breaking Genoa's resistance, Kevin Constant stupidly offered the hosts a route back into the game by getting himself sent off for throwing his forehead into the face of Cesare Bovo, who had chopped the Milan fullback down seconds beforehand. However, despite irs best efforts, Genoa could not force the goal that would have set up a frantic finale.