The mixed doubles will decide the tie winner.

Although Williams committed a host of errors during the match, she was happy to come away with the win.

"It's great to be back out in match day, and it's great to be back out here," Williams said.

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"I love playing in Australia. Some of my best memories are here.

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"It was my first match back [today], she played unbelievable. Maria is super young and such a good player.

"I was making a lot of errors. I was like, 'It's OK, it's your first match and you'll get better'. I just kept trying to think that."

Williams' appearance in Perth is her first tournament since her US Open meltdown, where she was handed a series of code violations in her loss to Naomi Osaka in the final.

The relaxed setting of the Hopman Cup is the perfect place for Williams to ease her way back into competition mode ahead of the Australian Open.

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Williams, who lost to her sister Venus in an exhibition match in Abu Dhabi last week, will be back in action on Tuesday night when the US take on the Roger Federer-led Switzerland.

Tsitsipas was left searching for answers after losing to world No.91 Cameron Norrie in straight sets in his opening match on Saturday.

But the 20-year-old handled the hot conditions far better on Monday, moving freely throughout the match as the temperature soared past 31 degrees.

"I felt a bit uncomfortable in the first match I played. I couldn't last long. I felt like I was out of breath," Tsitsipas said.

"But today I felt really comfortable playing the rallies. My shots felt better. In general I felt much more confident, and more me.

"Frances told me he felt the exact same thing I felt in my first match. I told him it was probably because of jet lag and the heat combined."

AAP