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World No.1 Iga Swiatek has scored resounding singles and doubles wins to lead Poland into the United Cup quarter-finals with a 2-1 victory over Team Spain.

World No.1 Iga Swiatek is locked ominously into grand slam mode after showing her class to pilot Poland into the quarter-finals of the $US10 million United Cup mixed teams event.

Swiatek hit the court under pressure on Monday, needing to win the women's singles rubber against Sara Sorribes Tormo to keep Poland's best-of-three-match tie with Spain alive.

Alejandro Davidovich Fokina had given the Spanish a 1-0 lead with a spirited 3-6 6-3 6-4 comeback victory over world No.9 Hubert Hurkacz at Perth's RAC Arena.

But Swiatek rose to the challenge with a crushing 6-2 6-1 win over Sorribes Tormo to force a deciding mixed doubles rubber.

The four-time grand slam champion and Hurkacz then needed barely half an hour to wrap up the tie 2-1 with a 6-0 6-0 drubbing of Sorribes Tormo and Davidovich to make Poland the first nation through to the quarter-finals, as Group A winners.

Poland and Spain both defeated Brazil in their other ties to set up Monday's winner-takes-all encounter.

Enjoying her 84th week atop the rankings, Swiatek is yet to drop a set in four Cup outings across singles and doubles, and even her partner was left in awe at Monday's display.

"Definitely she was carrying me through the whole day and was playing some amazing shots, just so consistent," Hurkacz said.

"Every single game she was making amazing shots, so it was a lot of fun."

All up, Swiatek has won 13 straight matches, including the WTA Finals decider against Aryna Sabalenka to wrestle the world No.1 spot back from the Belarusian.

The 22-year-old is fast firming as a hot favourite to add a first Australian Open crown to her grand slam collection this month.

"I'm really happy with my level and the way I'm focused," Swiatek said.

"I'm not feeling rusty. I'm not feeling like I need to get into a lot of rhythm.

"I'm playing freely, the same way I felt in Beijing, after the US Open.

"I'm just happy to be in that place."

Poland will face the best-performing runner-up from the four Perth groups in the opening Cup quarter-final on Wednesday, before the semi-finalists head to Sydney for Saturday's last-four showdowns.

After losing to Great Britain in their Group C opener, Team Australia beat Team USA 2-1 on Monday to secure a quarter-final berth.

In Sydney, three-time grand slam finalist Casper Ruud kept Norway's quarter-final chances flickering with victories in the singles and doubles against Team Croatia.

Donna Vekic had given Croatia an early 1-0 lead with a hard-earned 7-5 3-6 6-3 win over unheralded Malene Helgo.

But Ruud then clubbed Borna Coric 6-4 6-1 to send the tie to a decisive mixed encounter, which Norway claimed in a match tiebreaker.

The 6-2 3-6 10-7 victory for Ruud and Ulrikke Eikeri over Vekic and Ivan Dodig leaves Norway (1-1) anxiously awaiting the outcome of the last remaining Group F fixture between Croatia (0-1) and the Netherlands (1-0).

France opened their campaign with a 2-1 win over Germany.

The Germans, who beat Italy 2-1 on Saturday, were within one rubber of securing a quarter-final spot when world No.7 Alexander Zverev beat Adrian Mannarino 4-6 6-4 6-3 in the men's singles match.

World No.20 Caroline Garcia levelled the tie with a 1-6 6-2 6-2 win over Angelique Kerber.

France's paring of Garcia and Edouard Roger-Vasselin then prevailed in the mixed doubles 7-6 (7-4) 2-6 12-10 (match tiebreak).

France saved match point at 10-9 down in the match tiebreak.

"Crazy match, crazy end. So happy we got through," Roger-Vasselin said.

"We had two match points and they saved them with good shots. But really happy."