World number three Casper Ruud cruised past Thiago Monteiro in straight sets to give Norway some hope in their mixed teams United Cup tie against Brazil in Brisbane on Sunday.

After Brazil won both opening singles rubbers Saturday, Ruud's 6-3, 6-2 victory brought Norway back into the tie ahead of the second singles clash between his countrywoman Ulrikke Eikeri and Laura Pigossi.

Ruud was far too consistent for the 71st ranked Monteiro, who made 27 unforced errors, wrapping up a dominant win in only 70 minutes.

"It was a must-win match for Norway so I was maybe feeling the pressure a little bit," Ruud said. "But I was able to come out with a good start."

The Norwegian was a runner-up at last year's French and US Opens and said he was feeling confident ahead of the Australian Open later this month where he will bid to win a first Grand Slam title.

He did not play at Melbourne Park last year after rolling his ankle the day before his first match and said he wanted to make amends.

"I always feel very motivated coming down here playing in Australia. Last year was a bit unfortunate," he said.

"Hopefully I'll have a good start to the season down here and this is a perfect way for me to start the year on tour."

In Sydney, two-time Wimbledon champion Petra Kvitova proved too strong for Germany's Laura Siegemund, romping home 6-4, 6-2 in 1hr 49mins.

It ensured the Czech Republic won the tie with an unassailable 3-0 lead, having lost their opening clash with the United States 4-1.

"Playing Laura is always difficult. She's changing her game a lot, so I had to be ready for everything. I'm glad I got the point," said Kvitova, who beat American world number three Jessica Pegula earlier in the tournament.

"This group is very difficult but we are enjoying the event a lot and really happy that we (the Czech team) are all together here in Sydney."