Pegula’s win gave the USA a 2-0 lead against Poland, while Italy opened both games against Greece.
The remaining singles matches will be played on Saturday, with mixed doubles matches being held if necessary.
Italy’s Martina Trevisan prevailed 6-3, 6-7 (4), 7-5 in a thrilling 3 hour 14 minute match against world number 6 Maria Saccari.
The 27th-ranked left-hander appeared jubilant as he danced with joy at the Ken Rosewall Arena after the win, hugging teammates including Italian spearhead Matteo Berrettini.
“My God, it was a great fight today, I’m really, really, really happy. It was amazing,” Trevisan said. “Sometimes I had to smile because it calmed me down and helped me remember that life is good because I’m in this great stadium with so many people.
“I’m very happy about it because every day I keep working to improve and be better on the court and I think I deserved it today.”
Also, teammate Lorenzo Musetti defeated Stefanos Sakellaridis of Greece 6:1, 6:1.
Just as Trevisan’s encounter with Sakkari drew attention, Svitek’s defeat and his ordeal were the talk of the town.
Sviacek won all four of his matches against Pegula last year and will be hoping for a strong run at the Australian Open, which starts on January 16.
But Pegula, who was aggressive on her return, was no match for a solid performance that brought huge rewards for the world No.3.
Switek took a long bathroom break at the end of the first set and was able to win for the first time on his opening service game to start the second set.
But Pegula stayed focused and in form to secure a convincing victory.
Switek played down his emotional reaction and dismissed suggestions that travel from Brisbane to Sydney on Thursday had affected his performance.
“I wasn’t able to come out emotionally and physically, and I was kind of hopeless today,” Switek said.
“So it’s always difficult to lose, especially when you’re playing for your team and your country.”
Pegula, who reached the quarter-finals of three Grand Slams last year, said he knows the Ken Rosewall Arena well and the quick court action has benefited him.
The American was in Sydney for the group stage of the first tournament, while Poland and Italy played in Brisbane and Greece in Perth.
“I wanted to take it and use it as much as I could, and I thought I played aggressively, served smart and returned really well,” Pegula said.
Frances Tiafoe then defeated Kacper Zuk 6-3, 6-3 to give the USA a 2-0 lead over Poland.
Taylor Fritz could advance to the U.S. finals when she takes on world No. 10 Hubert Hurkac at third singles. A similar opportunity arose for Italy when Berrettini faced off against Greek star Stefanos Tsitsipas.
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