Iga Swiatek teamed up with Jan Zielinski for a decisive mixed doubles victory over Casper Ruud and Ulrikke Eikeri as Poland sealed Norway's elimination from the United Cup.

Swiatek got Poland off to a flawless start, overpowering Malene Helgo from the baseline in a crushing 6-1 6-0 win, which was wrapped up in just 63 minutes. 

Having made a losing start to their Group B campaign against Czechia, Norway needed Ruud to win his singles match against Hubert Hurkacz to force a decider. 

While he was nowhere near as dominant as Swiatek, the three-time grand slam finalist edged out Hurkacz 7-5 6-3 to give Norway a chance of salvaging their campaign.

Ruud has claimed all six of Norway's singles match wins at the United Cup. He is the only player with a 100% win share for his nation in singles games (min. five matches) at the event.

That meant the Sydney crowd was treated to a heavyweight mixed doubles decider featuring both Swiatek and Ruud, and it was the Polish pair that came through a topsy-turvy encounter victorious.

They triumphed 6-3 0-6 10-8, with Norway losing two crucial points on Ruud's serve at 8-7 up as they slipped to a second successive defeat. They can no longer qualify from Group B, which will be topped by the winners of Wednesday's tie between Norway and Czechia.

"Even though the second set was 0-6, we knew it was very close. It was a matter of single points, deciding points. We knew it could change at any moment," Swiatek's mixed doubles partner Zielinski said. 

"They had their momentum at some point, 8-7, serving with Casper, so we were not in the ideal position. 

"But we stayed tough, we showed some good returns and our best tennis when it mattered, so I'm happy with the outcome." 

Elsewhere, Stefanos Tsitsipas was beaten in both singles and mixed doubles as Kazakhstan swept Greece 3-0 to top Group C and clinch a quarter-final place.

Tsitsipas was stunned by Alexander Shevchenko in the opening match of the tie in Perth, with the world number 11 going down 6-4 6-3.

That teed up former Wimbledon champion Elena Rybakina to seal Kazakhstan's progress with a 6-4 6-3 win over Maria Sakkari, having powered into a 5-0 lead in the second set before ceding one of her breaks.

As she prepares for next month's Australian Open under new coach Goran Ivanisevic, Rybakina feels her participation in the tournament has been helpful.

"We've just been working a couple weeks together. This is our first official tournament," Rybakina said of Ivanisevic. "We're still getting to know each other a bit. He's a fun guy. 

"He gives some experience from when he played and also as a coach. I'm just happy to work with him. Hopefully, we'll have some good results together."

Greece's miserable outing was capped when Tsitsipas and Despina Papamichail suffered a 2-6 6-3 10-6 mixed doubles loss to Zhibek Kulambayeva and Aleksandr Nedovyesov.

In Group F, meanwhile, Katie Boulter helped Great Britain get off to a flying start with a 2-1 victory over Argentina, beating Nadia Podoroska 6-2 6-3 in the opening singles match.

Tomas Etcheverry levelled the tie with a 3-6 6-3 6-2 win over Billy Harris, but Boulter then teamed up with Charles Broom to beat Maria Lourdes Carle and Etcheverry 7-6 (7-4) 7-5 in the mixed doubles rubber.

Great Britain next face Australia on New Year's Day, in a tie that could see Boulter face her fiancé Alex de Minaur in the mixed doubles. 

"Let's hope we don't reach [the doubles] and we win before," Boulter said when asked about the prospect of facing him in a mixed doubles decider.

Finally, Germany and China both clinched qualification for the last eight, though Germany secured their spot as Group E winners with Alexander Zverev victorious in singles and mixed doubles in their 2-1 win.

Zverev rallied to beat Zhang Zhizhen 2-6 6-0 6-2 in the opening singles match of the tie, then partnered Laura Siegemund for a 6-2 7-6 (7-3) mixed doubles win over Zhizhen and Zhang Shuai.

Shuai had earlier beaten Siegemund in the women's singles to ensure China would also be present in the last eight.