Hubert Hurkacz gave Poland a 1-0 lead in the tie after defeating Alexander Shevchenko 6-3 6-2 in just 57 minutes.
World No.2 Swiatek had to fight much harder in her singles match against 2022 Wimbledon champion Elena Rybakina, but she was able to come from a break down in the opening set to post the 7-6 (7-5) 6-4 victory.
Swiatek had her upper right leg strapped after tweaking her thigh during her quarter-final singles win over Katie Boulter two days earlier, but the five-time grand slam winner got through Saturday's match OK to allay any injury fears.
The top-seeded US pairing of Taylor Fritz and Coco Gauff will start as hot favourites against Czechia's Tomas Machac and Karolina Muchova in Saturday night's semi-final.
But whichever of the nations make it to Sunday's decider, they will face a fierce challenge from Poland.
Hurkacz lost to Casper Ruud and Machac during the United Cup group stage, but has been on fire since.
The world No.16 defeated Billy Harris in straight sets during Poland's quarter-final win over Great Britain, and then sent down 10 aces to one against Shevchenko on Saturday.
The moment — United Cup (@UnitedCupTennis) @HubertHurkacz sealed the deal �#UnitedCup pic.twitter.com/APq3jY6Af9January 4, 2025
"From every single match I'm playing better and better. I'm happy with my performance," Hurkacz said.
World No.6 Rybakina broke Swiatek early in Saturday's semi-final battle and was serving for the first set at 5-3 up.
Swiatek broke back, and then had two set points on a Rybakina service game that lasted more than 13 minutes.
Rybakina eventually managed to hold, but Swiatek was too good in the tiebreak, taking the set in 72 minutes.
Swiatek broke to love in the seventh game of the second set and then saved a late break point to seal the 123-minute victory.Â
Team Poland fans cheered Hurkacz on in his quick win over Kazakhstan's Alexander Shevchenko. (Mark Evans/AAP PHOTOS)
"I for sure didn't start well. I felt like I was on a hand-break a bit," Swiatek said.
"I knew I had to do something because this match was going to go to waste.
Iga Swiatek secured the win for Poland with a 7-6 (7-5) 6-4 win over Kazakhstan's Elena Rybakina.(Mark Evans/AAP PHOTOS)
"I changed the momentum and I'm happy I did that in the last possible chance in the first set.
"It means a lot to me to be able to play today, especially after such an intense day (two days earlier in the quarter-final win over Great Britain).Â
"It's not easy to recover when you're going back to the hotel at 1am and falling asleep at 5am. So this win makes me really proud."
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