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Franck Kessie opened the scoring from the penalty spot in the first half before Brahim struck early in the second to secure a fourth win in four games in all competitions in 2020-2021.
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Zlatan Ibrahimovic was again absent after testing positive for coronavirus, but Stefano Pioli's men were in control throughout at Stadio Ezio Scida as they stretched their unbeaten Serie A run to 14 matches.
There was a blow for Milan, though, who saw Ante Rebic leave the pitch in the second half with a nasty arm injury sustained after he tripped and fell.
Milan's early control of possession yielded little in terms of chances, although a header from Simon Kjaer bounced off the turf and then the crossbar from Hakan Calhanoglu's corner.
As the half moved into injury time, Rebic was felled by Luca Marrone in the penalty area and, after the forward escaped a possible handball following a VAR check, Kessie made no mistake with an emphatic finish from the spot.
Milan doubled its advantage just five minutes into the second half, Brahim finishing low on the turn after the ball fell kindly to him in the six-yard box at the end of a swift break involving Alexis Saelemaekers and Calhanoglu.
Crotone did not lack endeavour but Gianluigi Donnarumma's goal was rarely threatened as the Serie A newcomer slipped to a second successive defeat.
