Milan tore 10-man Crotone to shreds with Patrick Cutrone, Franck Kessie and Suso, but the hosts saw red after just four minutes.
The game was without doubt changed when Federico Ceccherini saw red for bringing down Cutrone and Kessie converted the resulting penalty.
Teenager striker Cutrone, who has been linked with a loan move to Crotone, was inspirational and nodded in a second.
He then set up the third goal for Suso and the game was to all intents and purposes over by half-time.
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