World number two Iga Swiatek dug deep to overcome Katie Boulter in a tense three-set women's singles match as Poland reached the semifinals of the mixed teams United Cup after defeating Britain on Thursday.

Poland will now face Kazakhstan on Saturday, with a mouthwatering clash in prospect between Swiatek and 2022 Wimbledon champion Elena Rybakina.

Swiatek sealed Poland's quarterfinal victory in Sydney after surviving a near three-hour battle at Ken Rosewall Arena as she pushed through the pain barrier and a gritty performance from 24th ranked Boulter.

The five-time grand slam champion threw her racquet and raised both her arms in jubilation after prevailing 6-7 (4), 6-1, 6-4. It was Swiatek's third straight tournament victory in her return from a one-month suspension after testing positive for the banned substance trimetazidine.

In their first career meeting, Swiatek raced into a 3-0 lead in the first set, but Boulter was undaunted and matched Swiatek's formidable power from the baseline.

Boulter clinched a titanic 74-minute opening set in the tiebreak, but she could not sustain the intensity as Swiatek took control to force a deciding set.

Swiatek, however, was broken on serve early in the third set and had to take a medical timeout. She returned with her upper right leg strapped, but the Pole's famed resilience came to the fore as she finally broke Boulter's spirit.

"I am just exhausted, happy that I won," Swiatek said. "This match was crazy, so many changes of momentum. I'm happy that we won and will use the day off tomorrow."

Earlier, 16th-ranked Hubert Hurkacz had given Poland a flying start after a 7-6 (3), 7-5 victory over Billy Harris in the men's singles.

Even though he was ranked 109 places higher than his opponent, Hurkacz entered with reason to feel anxious, having lost both his singles matches in the group stage.

But the 27-year-old was dominant on serve and stepped up in the big moments late in both sets to prevail in the one-hour, 45-minute match.

"Today was a really difficult battle with Billy. He was playing some really great tennis and definitely really happy to get through this one," Hurkacz said. "This win is so crucial for me to get more confidence and get another match in."

Italy will play the Czech Republic in the quarterfinals on Friday, featuring an intriguing women's clash between world number four Jasmine Paolini and former French Open finalist Karolina Muchova.