The defending champions, who won the trophy last January over Italy, earned a 1-6, 7-6 (7/5), 10-7 mixed doubles win to claim victory in Perth after the sides split the singles.
"We have a team energy from last year here, we don't want to take a loss and let it die," said Fritz, who was broken twice in the opening set.
World number five Pegula added: "To get a win in this fashion after such a long day (on court) brings back a lot of memories.
"It was a big win today, especially after losing such a tough singles match."
Britain, who beat Australia to open their tournament account, took a 1-0 lead when Pegula crashed 5-7, 6-4, 6-4 to Katie Boulter in the singles.
It was Boulter's first win over a top-five player on her seventh attempt after she bounced back from a set and double-break down.
"This was a very hard match for both of us," said the 56th-ranked Boulter. "I play my best tennis when I'm smiling and having fun.
"I kept trying to get over the line. I thrive in a team atmosphere... so many tennis heads giving information. It helps you to think clearly."
Pegula's 10th-ranked teammate Fritz kept the tie alive despite a thigh strain he blamed on over-training, defeating Cameron Norrie 7-6 (5), 6-4.
"I strained something but got through it," said Fritz. "Cam and I have played so many times (14). It's always a battle, always close."
World number one Novak Djokovic opens his season for Serbia later against China's Zhang Zhizhen, with the Chinese team on a high after beating the Czech Republic 3-0.
In Sydney, Leylah Fernandez led Canada to a fighting victory over Chile with the former US Open finalist winning her singles rubber and then backing up in a decisive mixed doubles.
The 35th-ranked Fernandez got Canada off to a perfect start, cruising past Chile's Daniela Seguel 6-2, 6-3 in 73 minutes.
With Canadian number one Felix Auger-Aliassime sitting out the men's singles, 314th-ranked Steven Diez stepped up but was toppled by world number 19 Nicolas Jarry 7-5, 6-4.
It set up a deciding mixed doubles, with Fernandez teaming with Diez to battle past Seguel and Tomas Barrios Vera 7-5, 4-6, 10-8.
"I'm extremely happy with the way I played," said Fernandez, who was part of the Canadian team that won the Billie Jean King Cup for the first time this year.
The 21-year-old broke five times in her singles clash against a player in her first WTA Tour-level singles match in nearly two years, using the serve-and-volley tactic well.
"First match of the season so had some nerves, but happy with the way I was able to handle it," she said.
