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Simona Halep again did it tough while Elina Svitolina and Karolina Pliskova have both cruised into the third round at the Australian Open.

World No.1 Simona Halep is continuing to warm into the Australian Open, fighting her way to a third round berth at Melbourne Park.

Playing just her third match of the year after an extended break, Halep was again pushed to three sets on Thursday before overcoming promising young American Sofia Kenin 6-3 6-7 (5-7) 6-4.

Halep, who lost the final at Melbourne Park last year, was down a break at 2-4 in the deciding set but showed poise under pressure to claw her way back.

The French Open champion said in her post match interview that she injured herself during the second set.

"I have no idea how I won," the 27-year-old said.

"It was a very tough one - she is an amazing player."

Elina Svitolina and Karolina Pliskova also moved safely into the third round in another step in their quests to ditch the unwanted tag of "best current female player yet to win a major".

The sixth-seeded Svitolina proved too strong for Slovakian Viktoria Kuzmova, winning 6-4 6-1, while No.7 seed Pliskova ousted American Madison Brengle 4-6 6-1 6-0.

Svitolina has never been beyond the quarter-finals at grand slam level in 25 previous attempts, but shapes as a genuine contender at Melbourne Park, especially after her unbeaten run to victory at the WTA Finals in Singapore late last year.

"I was playing great tennis there, it gave me lots of confidence and I took lots of good stuff from that," said the 24-year-old, whose next opponent will be Zhang Shuai from China.

"I still have to work here and I'm up for the challenge."

Supporting Svitolina from her courtside box on Thursday was new boyfriend Gael Monfils.

The French showman's playing reputation as a largely unfulfilled talent should provide a cautionary tale for Svitolina as she seeks to deliver on her promise.

"He's there for me, he's there supporting me and I'm there for him as well," she said.

Pliskova's third-round opponent at Melbourne Park will be Italian Camila Giorgi, who belted Poland's Iga Swiatek 6-2 6-0.

Unlike Svitolina and Pliskova, Japanese star Naomi Osaka is already a major winner, having upset Serena Williams in last year's controversial US Open final.

The No.4 seed was largely untroubled on Thursday, easing past Slovenia's Tamara Zidansek 6-2 6-4.

Osaka's next opponent will be No.28 Su-Wei Tsieh from Taiwan who ousted German Larua Siegemund 6-3 6-4.

Latvian No.13 seed Anastasija Sevastova downed Canadian qualifier Bianca Andreescu 6-3 3-6 6-2.