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Reina, who was a late replacement for Gianluigi Donnarumma at Stadio Luigi Ferraris, gifted Lasse Schone an opener four minutes before the interval when he bundled in a free-kick.
Milan scored twice in the space of six second-half minutes to turn the game on its head, however, Theo Hernandez thumping in from a tight angle six minutes after the restart before Franck Kessie converted a penalty after a VAR (video assistant referee) check .
The referee, who also dismissed substitutes Riccardo Saponara and Samu Castillejo, deemed Davide Biraschi's handball for that penalty was worthy of a straight red card, although Milan's numerical advantage was cut when Davide Calabria received his marching orders.
Calabria's indiscipline looked set to cost Milan dearly when Reina charged in recklessly on Christian Kouame but, in another dramatic twist, the goalkeeper made a superb save from Schone's spot-kick to secure a vital triumph for Milan.
