Iran Press/ Europe: Davide Calabria crossed from the right for the France striker to head in the winner for the Rossoneri.
The defeat ended Juve's hopes of qualifying for the Champions League after they were docked 10 points earlier in the week.
Alexis Saelemaekers had a low shot saved by Juve's Wojciech Szczesny as Milan probed for a second goal.
Milan have won home and away against Juventus for just the third time in the last 50 years.
They are now secure in fourth place, with Inter, Lazio, and champions Napoli having already qualified for next season's Champions League.
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