The Rossoneri were left with a mountain to climb by some clinical finishing from Parma early on, with Marco Parolo's measured drive into the far corner putting the hosts ahead after 10 minutes.
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Andrea Poli came close to equalising soon after but Parma were able to counter ruthlessly to extend their advantage in first-half stoppage time, as former Milan forward Antonio Cassano guided home.
On the hour-mark Milan reduced the deficit through Alessandro Matri, who wriggled in his first goal for the club just moments after Walter Gargano struck the crossbar at the other end.
Milan's efforts looked to have secured a point but there was still late drama in store, as Parolo's stoppage-time free kick from all of 30 yards took a bounce before squeezing inside the near post.