Milan's sixth defeat in 12 league games left last season's runners-up in 13th place, with coach Massimiliano Allegri's future increasingly in doubt.
Lazio consolidated fifth place with a 3-2 win in the capital derby against Roma, as both teams had a player sent off.
In Germany, Bayer Leverkusen missed the chance to go above fourth-placed champions Borussia Dortmund after losing 3-1 to third-bottom Wolfsburg.
Leverkusen stayed a point above Hanover, who won 4-2 at Stuttgart.
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