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Title rival Inter drew 0-0 with Atalanta on Monday (AEDT), but Milan could not take advantage the following day as Spezia came from behind in incredible fashion.
Rafael Leao put Milan ahead after Theo Hernandez's penalty miss, but Kevin Agudelo levelled midway through the second half.
Milan were furious when Junior Messias' fine late effort was struck off due to a premature whistle from the referee, with Zlatan Ibrahimovic then hitting the crossbar.
And Gyasi had the final say, slotting home in the 96th minute to sensationally earn Spezia's first league win at San Siro.
