A fatigued world No.6 Casper Ruud has won his singles match but wasn't able to back up for the deciding mixed doubles as team Norway crashed to a 2-1 United Cup loss to Czechia in Sydney.

But Germany's title defence started in hot fashion, with world No.2 Alexander Zverev guiding his team to a 3-0 win over Brazil in Perth.

Czechia took a 1-0 lead in Sunday's tie with Norway at Ken Rosewall Arena after 2023 French Open finalist Karolina Muchova crushed world No.404 Malene Helgo 6-2 6-2.

It meant Ruud needed to beat world No.25 Tomas Machac to level proceedings, which the Norwegian star did with a 7-6 (8-6) 5-7 6-4 victory in two hours, 54 minutes.

Ruud was clearly tiring in the third set and received treatment on his legs in two consecutive changeovers.

The 26-year-old was rested for the mixed doubles, and Muchova and Machac took full advantage by powering Czechia to a 6-4 6-4 win over little-known Norwegian pairing Viktor Durasovic and Ulrikke Eikeri.

Muchova and Machac had fun in their doubles win, with the pair full of energy despite it being the second match of the day for both.

"We were just joking here and there to make it a bit lighter. Maybe it helped us there," Muchova said.

Ruud committed 31 unforced errors in his singles match but converted three of his five break-point chances to seal the win, with his new fiance Maria Galligani watching from the stands.

"I was a little bit tired towards the end. It hasn't been the longest of off seasons," Ruud said.

"I did get engaged. That's the biggest achievement of the year for sure.

"It was a great moment for me and my now fiance Maria. This was my first match as an engaged man, so I guess it's working well."

In Perth, Zverev and world No.21 Laura Siegemund produced singles wins to wrap up the tie for Germany against Brazil.

Siegemund defeated world No.17 Beatriz Haddad Maia 6-3 1-6 6-4 in two hours, 33 minutes, before Zverev eased past world No.109 Thiago Monteiro 6-4 6-4.

SMOOOOTH ?Zverev makes a cracking start to the second set after sealing the first 6-4 ??#UnitedCup pic.twitter.com/RvYhGiVSD1? United Cup (@UnitedCupTennis) December 29, 2024

A fit-looking Zverev snared a break early in each set on the way to the 78-minute victory before Siegemund and Tim P?tz wrapped up matters 7-6 (10-8) 6-4 over Rafael Matos and Carolina Alves.

In the first of Sunday night's two ties, Italy romped to a 3-0 win over Switzerland in Sydney.

Flavio Cobolli gave Italy a 1-0 lead with a 6-3 7-6 (7-2) with over Dominic Stricker in a battle of two exciting 22-year-olds.

Stricker's loss left comeback ace Belinda Bencic needing to beat world No.4 Jasmine Paolini to force a deciding mixed doubles rubber.

But Paolini, a two-time grand slam finalist in 2024, showed no mercy to Bencic in just the Swiss star's fourth tournament back from maternity leave, crushing the one-time world No.4 6-1 6-1 in less than an hour.

Switzerland could have sealed a quarter-final spot with victory.

Instead, Italy are now favourites to top Group D and advance with success over France on Tuesday after also winning the mixed doubles to complete the whitewash.

Australia's campaign started with a shock 2-1 loss to Argentina on Saturday night, leaving Alex de Minaur and company needing to beat Great Britain and his fiancee Katie Boulter on Wednesday night to have a chance to make the quarter-finals.