Berrettini watched Italy's 2023 victory from the sidelines as he recovered from an ankle injury that he sustained a few months earlier.
The former world number world number six spent six months on the sidelines and subsequently dropped out of the world's top 150.
However, he returned to action in March and quickly claimed three titles - the most he has ever won in a calendar year.
Now ranked 35th, Berrettini has been crucial to Italy's title defence this week, pairing up with Sinner to win the doubles decider against Argentina before triumphing in his semi-final singles match against Australia's Thanasi Kokkinakis.
He replicated his fine form against Van de Zandschulp, hitting 10 forehand winners and 16 aces on his way to victory.
"It feels unbelievable, it feels really great to be on court - being able to be health and enjoying this kind of atmosphere is the most important thing for me," Berrettini said.
"I missed these moments and that's why I'm really happy."