The AC Milan youngster, 19, netted twice in the first 45 minutes after Franck Kessie had given the Serie A giants the lead after just 14 minutes.
Carlo Ancelotti had named a strong side for the clash, including huge names including Mats Hummels, David Alaba, Franck Ribery, Thomas Muller, Kingsley Coman and Robert Lewandowski.
But Milan tore them apart in the opening period as teenager Cutrone put them to the sword.
The Italians were showing off a couple of new signings, including former Premier League flop Fabio Borini and ex-Wolfsburg man Ricardo Rodriguez.