Berrettini powered past Brazilian No 1 Thiago Monteiro 6-4, 7-6(7) to give Italy a 2-1 lead in their United Cup opener.
His win ensured that Bronzetti could claim the tie with victory over Laura Pigossi and she obliged with a 6-0, 6-2 triumph.
"Pretty happy I have to say. It's been a long time since I've played my last singles match, so I didn't know what to expect. I think the level was pretty high," Berrettini said.
"I'm happy for my performance, but obviously when you play in these kind of competitions the most important thing is to get the win and bring a point for the team and that's why I'm even happier.
"It's all about the heart, especially when you're playing for Italy. When you see your teammates in the box, you have to give a little bit more and that's what I tried to do.
"Always playing tough matches against Thiago, really tough player. But I think I played better in the important moments and that's why I won."
Later, US No 2 Frances Tiafoe secured victory for his team against the Czech Republic at the United Cup when Tomas Machac retired due to an ankle injury.
Tiafoe led 6-3, 2-4 after 89 minutes when Machac turned his ankle and went down in a heap.
It proved an anti-climactic way for the USA to clinch victory in the tie after Petra Kvitova dug deep to keep the Czech Republic alive.
Kvitova would save seven set points in the opening set on her way to defeating World No 3 Jessica Pegula, 7-6(6), 6-4 in Sydney to make it 2-1 in the United Cup tie.
"We keep fighting," Kvitova said. "I think USA is such a great team with great players in the team. We are not really favorites here, but we are fighting every match, every point. That's our team spirit."
Pegula used the dead rubber mixed doubles match to rebound from her singles disappointment and she and Taylor Fritz came through a super-tiebreak to beat Marie Bouzkova and Jiri Lehecka, 2-6, 6-3, 10-7 and round off a 4-1 victory.
"I feel like on our team there's a lot of different options and different pairings and the mixed could be important down the line," Fritz said.
"We want to figure out what will be our best team or at least get the rust off. The whole thing can be decided by the mixed doubles so we want to know who we want to go with in a big match."