Berrettini broke Ruud once in each set for a clean 6-4, 6-4 win that gave Italy an unassailable 3-0 lead over Norway going into the second women's singles and mixed doubles.
Italy will face either Poland or Switzerland in the Brisbane final, the winner of this game will be known later on Tuesday.
The winner of each city's final in Sydney, Brisbane and Perth will play the semi-finals in Sydney, with the top performing team from among the beaten finalists.
Ruud, who had a brilliant 2022, started as a slight favorite, but Berrettini came into the game in great shape.
He served well throughout the game and his powerful shots from the baseline put enormous pressure on the Norwegian.
Berrettini hit 10 aces and eight forehand winners.
The Italian player, who slipped to 16th in the world, said he knew he had to serve well against Ruud.
"He improved so much last year that I knew I had to give my best," he said.
In Sydney, the American Jessica Pegula, world No.3, largely beat the German Laura Siegemund 6-3, 6-2.
Frances Tiafoe edged Oscar Otte 7-5, 6-4 as the Americans beat Germany 4-0.
The United States will play Great Britain in the Sydney City Final.
In Perth, Greece and Belgium are tied 1-1.
The Greeks must win or lose 3-2 to qualify for the city final against Croatia or France.
© 2023 AFP