"I've never been a defending champion before, that's new and I was really nervous", said Osaka, who booked a third-round meeting with American Danielle Collins, who was a 6-4, 6-1 victor over Kirsten Flipkens.
The match was Osaka's first as the world's top player and as the reigning Australian Open champion - and she was contesting it coachless after parting ways with Sascha Bajin shortly after her Melbourne triumph.
"I've never been a defending champion before - that's new and I was really nervous", said Osaka, whose first WTA title at Indian Wells a year ago launched a 2018 campaign that would eventually include her first Grand Slam crown at the US Open. And I think I created some opportunities.
And the Japanese's eagerness to get her title defence off to a flyer led to butterflies, with Osaka suffering a scare before emerging with a 6-3, 6-4 last-64 victory over France's Kristina Mladenovic on Saturday.
When I see someone at the net, I just start thinking percentages, like, you know, 30% chance they are going to go this way, so might as well go with the higher chance - or she went this way last time, so she might go this way the other time.
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"It was really hard against her because I never played against her - it was a bit hard to get a rhythm", Halep said.
Williams pulled off the unlikely comeback despite failing to produce a single ace although she said her varying serve speeds were "what I needed to do".
"I was playing really aggressive", Kerber said.
The German had already broken four times and was in complete control before Klizan called it quits. "I was just fighting in the first set to find that balance between being aggressive and not rushing too much".
Earlier, Roger Federer beat Peter Gojowczyk 6-1, 7-5 in the second round. It feels like the ball stops for a split second while I am thinking about that.
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Rife, a 23-year-old comedian and actor, and Beckinsale, 45, dated back in 2017. A lot of ups and downs but she's moved on and I'm happy.
Despite Kvitova firing down 10 aces, it was nullified, as she also hit ten double faults, gifting Williams the free points.
The 38-year-old veteran American broke the Czech once more in the match's final game, letting loose with a euphoric scream as she sealed one of her most impressive victories in recent memory.
He'll play Guido Pella, who ended the hopes of another Aussie qualifier, Alex Bolt, 7-6 (7/5), 2-6, 6-3.
Eighth-seeded American John Isner raced into the third round with a 6-0, 6-2 victory over Australian qualifier Alexei Popyrin.
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At one point he looks at the camera and screams that "it's stupid" to think he would hold women against their will given his past. Asked about their relationship with Kelly , Azriel Clary , 21, sobbed in a CBS television interview due to be aired on Thursday.