The world No.16, who lost in the semi-finals of last year's Australian Open to eventual champion Rafael Nadal, used his powerful serve to dominate the Norwegian in a 6-4 6-4 win on Tuesday.
Berrettini hit 10 aces and won 88 per cent of points (35 of 40) when landing his first serve to move to 2-0 after his tournament-opening defeat of Brazilian Thiago Monteiro.
"Casper, he's a super-solid player, he improved so much in the past year, so I knew that I had to serve my best," Berrettini said.
"We know each other pretty well, so we're kind of always studying what we're doing and I knew that I had to serve like that.
"But it's one thing knowing and one (other) thing doing it."
His victory in 86 minutes put Italy up 3-0 against Norway, which was good enough for top spot in their group with two matches remaining in their tie.
Italy will play either Poland or Switzerland - who are locked at 1-1 ahead of Tuesday's clash between Hubert Hurkacz and Stan Wawrinka - in Wednesday's city final at Pat Rafter Arena.
The winner will travel to Sydney for semi-finals from Friday.
"The goal is to have the longest run possible. It's super nice to play with my teammates," Berrettini said.
"The other day at dinner we were talking about when we were 12 playing against each other. It's super nice and I'm really happy. It's the first time obviously playing with the girls and I think it's special, different, maybe a little bit more stressful, but we're enjoying it a lot."
In Sydney, Jessica Pegula eased past Germany's Laura Siegemund 6-3 6-2 to clinch the tie 3-0 in a dead rubber. The United States had already booked their city final berth with Britain on Monday.
In Perth, Greece secured a city final when Maria Sakkari beat Elise Mertens to earn the final point they needed from the first of three chances in matches against Belgium.
The world No.6 won 6-1 7-5, following Stefanos Tsitsipas's impressive dismantling of David Goffin on Monday.
The winner of the tie between France and Croatia will advance as the other Perth finalist, with Croatia leading 2-0 after Monday's results.