In a rematch of their U.S. Open quarter-final and Gstaad final, where world number three Ruud prevailed last year, it was Berrettini who took control of the match on the back of his powerful serve to seal a 6-4 6-4 Group E win.
"Casper, he's a super solid player, he improved so much in the past year. I knew I had to serve my best," Berrettini, who fired 10 aces and won 88% of points on his first-serve, said.
"We know each other well, so we're always studying what we're doing and I knew that I had to serve like that. One thing is knowing and one thing is doing it, but I'm really glad it worked out pretty well."
Berrettini's victory over the French Open and U.S. Open runner-up gave Italy an unassailable 3-0 lead and they went on to sweep the tie as Lucia Bronzetti and the pair of Camila Rosatello and Lorenzo Musetti won their matches.
The winners of each of the two groups from the three venues - Sydney, Perth and Brisbane - compete in the "city finals" on Wednesday to determine who makes the last four.
The fourth semi-finalist will be a runner-up with the best record from their three matches in the $15 million event.
Britain won both their Group D matches to set up a meeting with Group C winners United States, who completed a 5-0 win over Germany as Jessica Pegula and Frances Tiafoe won their singles matches before teaming up for more success in mixed doubles.
Poland set up their meeting with Italy when Magda Linette rallied to beat Switzerland's Jil Teichmann 5-7 6-4 6-1 to give her country a 3-1 advantage that secured the tie and top position in Group B.
World number 10 Hubert Hurkacz earlier beat Swiss veteran Stan Wawrinka 7-6(5) 6-4 to send Poland on their way.
Maria Sakkari earned Greece a spot in the Perth final from Group A with a 6-1 7-5 win over Belgium's Elise Mertens.
The Greeks wrapped up the tie 4-1 with Sakkari and Stefanos Tsitsipas comfortably winning their mixed doubles rubber after Stefanos Sakellaridis beat Zizou Bergs.
Up next for them are Croatia, who took a decisive 3-1 lead over France as Borna Gojo battled from down 5-3 in the third set to outlast Adrian Mannarino 7-6(5) 3-6 7-6(5) in an epic battle that lasted almost three hours.
