Montella’s side won 4-3 on penalties after a 1-1 draw in Doha, Gianluigi Donnarumma making a crucial spot-kick save from Paulo Dybala, who had blazed a gilt-edged chance over the bar towards the end of extra time.
Milan sit fifth in the Serie A table, having picked up a solitary point from six available before the winter break.
And Montella, who masterminded a 1-0 win over the five-time defending Italian champions Juve in October, hopes this latest success is just the beginning for his youthful side.
“It’s a nice feeling to win,” Montella told Rai Sport.
“The lads have to see this as a good starting point for the future, as we played on a par with a great side like Juventus.
“I am very happy for President Silvio Berlusconi, as we know how much he cared about this trophy and we dedicate it to him.
“In the first 20 minutes we weren’t our usual selves, but we shrugged off the tension and slowly improved as the game wore on. We created many chances and deserved to win in 90 minutes.
“Fatigue set in and we dipped in terms of intensity during extra time, but to lose when Paulo Dybala had that chance at the end would’ve been cruel.”