Swiatek gave Poland a 1-0 lead in the mixed teams tournament tie with a commanding 6-1 6-3 win in Brisbane on Saturday.
The 21-year-old saved a break point in the opening game and was never troubled from there.
She displayed the sort of intensity, focus and aggression that led her to eight singles titles in 2022, including the French and US Open crowns.
"I'm pretty happy with my performance," Swiatek told the Nine Network.
"You know, first matches of the season are always kind of rusty, so I'm happy that in the important moments I was really composed.
"I tried to have some initiative and just push a little bit more.
"I'm happy with the game and I'm pretty happy to be here because the venue is amazing and I really love the stadium.
"Having my team behind my back is something else."
Swiatek went on a 37-match winning streak last season - the equal-longest in women's tennis since Steffi Graf in 1990.
But she revealed on the eve of the United Cup that she initially struggled with taking on retired Australian ace Ash Barty's world No.1 mantle.
Swiatek hopes to take her game to a new level in 2023 and has hit the ground running ahead of next month's Australian Open.
Swiatek was a semi-finalist at Melbourne Park last summer, losing to American Danielle Collins.
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