The defending champions, who won the trophy last January over Italy, earned a 1-6, 7-6(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."
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.
Ranked 35, she got her country off to a perfect start in their Group B tie in Sydney, 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.
She 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.
Diez put up a decent fight against Jarry but brief lapses at the end of each set proved his downfall.
"Steven is a grinder, a very tough player," Jarry said. "So it was a tough match for the first one of the year."
