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Giampaolo Pazzini came close to making the breakthrough in the sixth minute when he was played in by Kesuike Honda and chipped the ball over the on-rushing keeper, but his attempt was headed off the line.
The Rossoneri were dominating the early exchanges and opened the scoring in the 12th minute.
Honda was the next to threaten for Milan midway through the half when he was picked out on the edge of the box by Kevin Constant, but he could not get enough power on his low strike to beat the keeper.
Pazzini came close to adding a second at the end of the half when he saw his header saved by the keeper, as Milan held on to lead at the break.