Kulusevski scored Juve’s third in the 78th on a counterattack after being set up by Chiesa, who completed the rout in injury time by dribbling around the goalkeeper to deposit the ball into an empty net.
Juventus is seeking a record-extending 14th Cup title after losing last season’s final to Napoli.
Earlier, 10-man Atalanta beat visiting Lazio 3-2 and will next face either Napoli or Spezia, who play Thursday.
Aleksei Miranchuk scored the winner for Atalanta four minutes after teammate José Luis Palomino was shown a direct red card for a foul on Manuel Lazzari.
Berat Djimsiti and Ruslan Malinovskyi also scored for Atalanta in an entertaining match that included Lazio goals from Vedat Muriqi and Francesco Acerbi.
Atalanta forward Duvan Zapata could have added a fourth goal but had a penalty kick saved by Pepe Reina.
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