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Lorenzo Tonelli put the home side ahead after 10 minutes with a precise header from a corner which clipped the inside of the post before rolling over the line.
AC Milan's evening became even worse when Marco van Ginkel was forced from the field with an injury.
Verdi then wasted another glorious opportunity to put the game out of reach when he miscued a header and sent it over the bar, and was made to pay on the stroke of half time.
Torres, who was denied by a remarkable Luigi Sepe save in the 41st minute, opened his AC Milan account just two minutes later with a powerful header which was forced into the top corner from a difficult angle.