MELBOURNE, Australia - Reigning US Open champion Naomi Osaka is through to the third round in Melbourne after needing two sets to move past Tamara Zidansek.

The Japanese No.1 was tested by Zidansek, especially in the close second set, but she came up with big tennis at key moments to claim the 6-2, 6-4 win.

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Osaka is one of nine players in contention who could overtake Simona Halep and claim the WTA World No.1 ranking at the end of the fortnight - she would have to reach the Australian Open quarterfinals for the first time in order to have a chance.  

She took a positive step in that direction on Thursday against Zidansek, weathering a brief rain delay to play under the closed roof at Margaret Court Arena.

"I didn't think I played bad," she said. "I know I could have made fewer unforced errors, so that's the biggest take away.

"I feel like she played really well. I hadn't seen much of her before this match, so I had to do a lot of research.

"When I go into matches like these, where I feel like I'm expected to win, I always think the other player's going to play unbelievable. I feel that mentality's helping me a lot."

Osaka’s relentless attack earned her an early reward, breaking in the first game as she left no Zidansek second serve unpunished. The Slovenian, however, capitalized on a couple of loose errors from Osaka to earn a break of her own at 2-2 - looking keen to carve her way into the contest.

But the Japanese player got back on course right away with a break straight back, her heavy firepower keeping Zidansek on the back foot. Osaka reeled off the last three games in a row to close out he opening set.

Osaka found herself having to come back from 2-4 down in the second set as Zidansek started to find her range, hitting with more confidence and pace. Osaka responded in style, reeling off three games in a row to serve for the match - but things got a bit complicated again as Zidansek fought her way to two break points at 5-4.

Once again, the US Open champion calmly maneuvered her way out of trouble, responding with an ace and an unreturnable serve before sealing the match after 64 minutes on court.

With the victory, Osaka books a third-round clash with No.28 seed Hsieh Su-Wei, who edged past Laura Siegemund 6-3, 6-4 yesterday.

The Japanese forecasts a difficult match.

"I've played her once before but it was on grass," she said. "Playing her will be hard because she slices a lot, so I'll have a lot of practice tomorrow."