Juve had wrapped up the league title in April, for the fifth season in a row - and needed the Coppa Italia to make history.
Milan's 19-year-old goalkeeper Gianluigi Donnarumma was at fault as he fumbled in Douglas Costa's second and then spilled Mario Mandzukic's header for Benatia to poke home.
Juventus left no chance for Milan in the final match of the Italian Cup.
"At this moment Donnarumma is the Milan goalkeeper, the rest is down to the club", Gattuso told Rai Sport.More news: Pakistan, Ireland historic test begins in Dublin today
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"The lads had an extraordinary game and deserved this win".
As the two sets of players shook hands, Buffon touched Donnarumma's face before whispering a message in his ear.
Morocco global Mehdi Benatia broke the deadlock for the hosts 10 minutes into the second stanza with a free header inside the box, 1-0.
An own goal by substitute Nikola Kalinic completed a calamitous defensive display by Milan. Both are still fighting for their place in the table - Juve for the first spot and Milan for the final European place. "We have a winning mentality", said Benatia, who had come in for criticism after letting in Kalidou Koulibaly's goal in a 1-0 defeat to Napoli two weeks ago. I don't think the result is fair since we played very well in the first half.