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Milan almost took the lead in the 20th minute of the match as Adil Rami fired an effort towards goal that whistled narrowly over the crossbar.
They wouldn't have to wait much longer for the opener, however, as Riccardo Montolivo broke the deadlock in style with a long-range piledriver into the bottom corner.
Both sides struggled to create an opening in the second half, but Catania's hopes of getting back into the match took a major blow when Fabian Rinaudo was given his marching orders for a second yellow card 12 minutes from time.
Milan almost wrapped up all three points in the 88th minute as Taarabt picked up the ball on the edge of the box before sending an effort narrowly over the crossbar.
They came close again just two minutes later, but once again the shot was just too high after Balotelli had created space for himself to go for goal.
There was no late drama on Catania's side, however, as Milan moved into the hop half of the table with a fourth straight win, while Catania remain eight points from safety.