Gauff picked up from where she left off at the WTA Finals with a clinical 6-3 6-2 win over former US Open finalist Leylah Fernandez at RAC Arena on Sunday night.
The world No.3's impressive victory, completed inside 90 minutes, put the US 1-0 up over Canada in their opening Group A tie.
Gauff ended the 2024 season with a bang, backing up her eighth WTA title at the rich and prestigious China Open in Beijing with an even bigger triumph at the WTA Finals in Saudi Arabia.
The 20-year-old took down the second-ranked four-time grand slam winner Iga Swiatek and world No.1 Aryna Sabalenka in consecutive matches en route to the title and shapes as the pair's greatest threat at next month's Australian Open.
Fernandez boasted the second-most hardcourt wins in 2024, behind only two-time AO defending champ Sabalenka, and had upset Paris Olympics silver medallist Donna Vekic in her opening United Cup outing on Saturday.
But Gauff had too much firepower, especially on serve.
The 2022 US Open champion won 92 per cent of points after landing her first serve in the first set, and continued the onslaught in the second to leave Canada in serious danger of losing top spot in their group following a 2-1 victory over Croatia in their opening tie.
"Very happy," Gauff said of her Cup debut.
"Leylah played a great match. I knew going in it was going to be a tough match but I'm super happy with how I played and happy to get a point on the board for my team."
Felix Auger-Aliassime must upset world No.4 Taylor Fritz in the men's singles match to deny the US victory.
Fritz, who made his maiden grand slam final in New York in September, boasts a 2-0 win-loss record against Auger-Aliassime.
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