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Poland trailed after Lorenzo Musetti and Matteo Berrettini secured wins against Daniel Michalski and Hubert Hurkacz respectively, only for Swiatek and Magda Linette to level things with respective singles victories over Martina Trevisan and Lucia Bronzetti.
That sent the Brisbane city final to a decider in the mixed doubles, which Swiatek and Hurkacz won with ease 6-1 6-2 against Musetti and Camilla Rosatello, though there was a pause in the second set to dry rainfall on the court.
Despite defeat, Italy also advanced to the final four as the city finals loser with the best record.
It was more routine in Sydney as the United States eased to a 4-1 win against Great Britain.
Madison Keys came from a set down to beat Katie Swan, while Jessica Pegula eased past Harriet Dart 6-2 6-0 after Cameron Norrie had defeated Taylor Fritz in three sets.
Despite going a set behind, Frances Tiafoe came back to beat Dan Evans 3-6 7-5 6-3 to clinch the win for his country, before Pegula and Fritz added some gloss after beating Dart and Evans in the mixed doubles.
The third city final in Perth included a thriller as Greece's Stefanos Tsitsipas beat Borna Coric 6-0 6-7 (4-7) 7-5. Donna Vekic had no trouble getting Croatia on the board as she eased past Despina Papamichail 6-2 6-0.
Maria Sakkari put Greece 2-1 ahead when she beat Petra Martic 6-3 6-3, but Borna Gojo defeated Stefanos Sakellaridis in straight sets to make it 2-2.
However, Greece secured the win and their place in the last four after the pairing of Sakkari and Tsitsipas saw off Martic and Gojo 7-6 (8-6) 6-4.
Greece will take on Italy in the semi-finals, while Poland face the USA, with both taking place in Sydney on Friday.
