The win is Milan's seventh in its last eight league games and takes the Rossoneri one point above second-place Juventus.
Genoa managed to generate very little in attack over the course of 90 minutes, and Nocerino had the best chances of the first half to put Milan in front, only to be denied by goalkeeper Sebastien Frey.
The visitors began to take control of the game as the second half started, and a poor challenge from Genoa's Kakha Kaladze on Ibrahimovic inside the penalty area handed Milan a penalty kick and earned the former Milan man a second yellow card.
Ibrahimovic smashed home his spot kick to put Milan in front, and Genoa was able to offer nothing in return with just 10 men.
Robinho should have doubled the lead as he lifted the ball over the crossbar from a few yards, but Kevin-Prince Boateng set up Nocerino's fifth goal of the campaign in the 79th minute when he pulled the ball back from the end line across the face of goal for a simple tap in.
Juventus will try to take back the league lead on Sunday when the club hosts second-from-the-bottom Cesena, while third-place Udinese tries to keep pace with a visit to the San Siro on Saturday to face Inter Milan.
Napoli has drawn its last three games to slip to sixth in the table and the club hosts last-place Lecce in the other match on Saturday.
Also on Sunday, fifth-place Palermo travels to Parma, Roma tries to snap a spell of three losses in five games when the team visits Fiorentina, Catania and Cagliari meet up at the Angelo Massimino, Bologna entertains Siena, Atalanta brings a three-game unbeaten streak into its match with Chievo and Lazio rounds out the weekend on Monday with a home contest against Novara.