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It was the visitors who were the first to threaten the opposition goal as Pablo Barrientos picked up the ball on the edge of the box before firing a shot towards goal that Christian Abbiati had to save.
Milan came close to opening the scoring in the 20th minute as Adil Rami sent an effort whistling narrowly over the Catania crossbar.
The goal did come just four minutes later, however, as Riccardo Montolivo collected a pass before drilling a fine strike past the keeper and into the bottom corner.
The hosts almost had a second shortly after the half-hour mark as Adel Taarabt found himself unmarked on the edge of the box, only to fire his effort just past the post.