With the tie finely poised at 1-1 after Saturday’s games, on Sunday Hurkacz earned a crucial win, beating Alexander Bublik 7-6(8), 4-6, 6-3 to give No. 2 seed Poland a 2-1 lead.
Next up on the Pat Rafter Arena in Brisbane were Poland’s Magda Linette and Kazakhstan's Zhibek Kulambayeva.
The Pole, ranked 48th in the world, overpowered her opponent, winning 6-2, 6-1 to give her team an unassailable 3-1 advantage.
Hurkacz and Świątek then stepped onto the court for mixed doubles, seeing off Kulambayeva and Grigoriy Lomakin 6-3, 6-4 as Poland completed a 4-1 win over Kazakhstan.
Poland next face their other opponents in Group B of the United Cup, Switzerland.
The winners are set to qualify for the next stage of the tournament, the so-called City Final.
The two-day tie begins on Monday, with Świątek pitted against Belinda Bencic, while Hurkacz will entertain Stan Wawrinka on Tuesday.
The United Cup
The United Cup is a new mixed-teams event featuring 18 countries, who battle it out in the Australian cities of Brisbane, Perth and Sydney, WTA said.
The ties are played over two days, comprising two ATP and two WTA singles matches and one mixed-doubles match, according to officials.
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Source: TVP Sport, wtatennis.com, unitedcup.com