Poland's world No. 2 Iga Świątek secured the decisive point by beating Germany's Eva Lys 3-6, 6-3, 6-4 in the women's singles.
"It was tough" Świątek said after the match. "She was really going for it, especially in the first set."
"It's not easy, the first match of the season, but I'm happy we won," she added.
Hubert Hurkacz earlier gave Poland a 1-0 lead by defeating German world No. 3 Alexander Zverev 6-3, 6-4 in the men's singles.
Hurkacz’s victory marked his first competitive match since June, following knee surgery.
"It’s been a while since I've been competing," Hurkacz said. "For seven months we didn't know when I could get back on court. Today I was just trying to enjoy every moment."
Now ranked 83rd in the world, Hurkacz said serving well helped him regain confidence.
"It’s a nice feeling to find a good rhythm again," he said.
In the mixed doubles, Poland's Jan Zieliński and Katarzyna Kawa completed the sweep with a 7-6, 6-3 win over Zverev and Laura Siegemund.
The singles victories had already given Poland an unassailable lead before the doubles match.
Poland will face the Netherlands on Wednesday in Sydney in a bid to reach the quarterfinals.
The Dutch lost 0-3 to Germany on Sunday.
Eighteen national teams are competing in Sydney and Perth, divided into six groups of three. Group winners and the best runners-up from each city advance to the quarterfinals.
The United Cup serves as a warm-up event for the Australian Open, which begins on January 18 in Melbourne.
(gs)
Source: IAR, PAP