Poland reached the quarterfinals of the mixed-teams tournament thanks to a 2-1 win over Spain in Perth on New Year's Day.
Świątek beat Sara Sorribes Tormo 6-2, 6-1 in her singles match, before teaming up with the No. 9-ranked Hubert Hurkacz to defeat Tormo and Alejandro Davidovich Fokina 6-0, 6-0 in the doubles.
This gave Poland a 2-1 victory; Spain had led 1-0 after Davidovich Fokina beat Hurkacz 3-6, 6-3, 6-4.
The Polish team finished top of Group A, after earlier defeating Brazil 3-0.
Poland, who reached the last four in the 2022/23 United Cup, now face China in the quarterfinals, also in Perth, on Wednesday.
In other last-eight matches, France play Italy, Greece take on Canada and Australia face Serbia.
The 2023/24 United Cup runs until January 7, with the final due to be played at the Ken Rosewall Arena in Sydney.
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Source: United Cup, ESPN, Eurosport