Gauff opened with a statement 6-4, 6-4 win over Swiatek in 1hr 51min of hard-hitting tennis to fire a warning shot ahead of the Australian Open.
Big-serving Fritz then battled through against Hubert Hurkacz 6-4, 5-7, 7-6 (7/4) to spark wild celebrations as the Americans won the mixed-teams cup for the second time in three years after winning the inaugural event in 2023.
For Poland it meant falling at the final hurdle again after losing to Germany 12 months ago.
Gauff set the ball rolling with a second victory in a row over Swiatek after beating the former world number one at the WTA Finals in Riyadh on her way to the title.
Gauff had won all six of her previous singles and doubles matches this week and continued her streak when Swiatek double-faulted on match point at 4-5, 30-40 in the second set.
"I think I have the belief that I am one of the best players in the world, and when I play good tennis, it's hard for me to be beaten," said Gauff, who won the award as player of the tournament.
'Tough today'
The 20-year-old will go into the first Grand Slam of the year next Sunday unbeaten in singles since losing to world number one Aryna Sabalenka in the Wuhan semi-finals in October, and brimming with confidence.
"Today I think I played great tennis, and I'm happy to get a point," she said. "It was tough today. I'm not gonna lie."
Gauff's victory left the United States one win away from lifting the title for the second time, and Fritz delivered after edging a third-set tiebreak to seal a tense encounter.
"It's been a great week," said Fritz.
"They're an incredibly tough team and the margins are very small," he added after a serve-dominated match that featured 30 aces and just three break points.
"I feel like it could have always gone either way. Just want to say thanks to my whole team."
Earlier, Swiatek took a medical timeout at 5-4 down in the second set to have strapping put on her niggling left thigh which has bothered her all week in Sydney.
After losing to Gauff, Swiatek left the court in tears, walking gingerly, but returned laughing and joking during the trophy presentations.
Red-hot Gauff, who did not drop a set in five singles matches, goes into the Australian Open as world number three.
She enjoyed United Cup singles wins over Leylah Fernandez, Donna Vekic, Zhang Shuai, Karolina Muchova and Swiatek.
Fritz, who is at career-best number four in the rankings, dropped his opening United Cup match to Felix Auger-Aliassime but then won four straight.
