Goals in either half from Giampaolo Pazzini and substitute Mario Balotelli earned the Rossoneri all three points, despite a red card for visiting defender Kevin Constant.
That was not the game's only controversy, with the hosts demanding two penalties in the first half, but Massimiliano Allegri's side held on to secure the three points at the Stadio Luigi Ferraris.
M'Baye Niang had the first chance to put the visitors in front, but Genoa goalkeeper Sebastien Frey was equal to his attempt.
A foul by Daniele Portanova on Pazzini then saw the Genoa defender booked. The Milan striker limped on, with Balotelli told to warm up on the touchline.
Before the substitution could be carried out, though, Pazzini managed to put his side ahead with a powerful shot which went in off the underside of the crossbar.
His celebration towards the Genoa fans did not go down too well, but the home fans were soon more disillusioned when the referee did not award a spot-kick after the ball struck Niang's arm inside the penalty area.
A push on Andreas Granqvist shortly after was also missed by the officials, further infuriating the home faithful.
That frustration turned to disbelief when Cesare Bovo's direct free-kick hit the post for the luckless hosts.
Ciro Immobile was introduced in place of Mattia Cassani on the hour mark by Genoa coach Davide Ballardini as he searched for a goal, which came within seconds of the former Pescara forward's introduction - but at the other end.
A misplaced pass by Immobile set up the Milan attack, which was finished by Balotelli, who left Frey no chance with his instant, diagonal shot.
Tempers flared soon after with Constant picking up his second yellow card after a clash with Bovo.
The home side had a few chances to reduce the deficit, with Granqvist moving into a more advanced position to give even more weight to their attack.
However, despite their best efforts, they were unable to find a route back into the game and they remained just five points above the drop zone, while Milan climbed to within two points of Napoli ahead of their clash at Chievo on Sunday.