Zlatan Ibrahimovic scored from the spot to give the Milan club the lead but Massimo Maccarone brought the hosts back into the match.
Inter regained the advantage through Esteban Cambiasso on the stroke of half-time and Ibrahimovic then grabbed his second shortly after the restart. A late strike from Fernando Forestieri ensured a nervy finish for the defending champions, but they clung on for their 14th win of the season.
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