Right back Joshua Kimmich found Goretzka with a defence-splitting pass deep into stoppage time and the Germany midfielder coolly slotted the ball past Gianluigi Donnarumma to give the club a second win in the exhibition competition.
Dutch great and Bayern Munich legend Robben retires from football
Milan had their chances in the second half, not least when Patrick Cutrone was put through one-on-one with Sven Ulreich only to be denied by the goalkeeper, but could not find an equaliser on a warm night in Kansas City.
The match was Milan's first since head coach Marco Giampaolo took the helm at the Serie A club, who parted ways with Gennaro Gattuso at the end of last season.
Bayern consider signing Ousmane Dembele
Next up for Bayern Munich is a semi-final clash with Turkey's Fenerbahce on Tuesday while Milan face Portuguese outfit Benfica on Sunday.
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