The No.2 seed's campaign looked almost over on Wednesday when she slipped to 2-5 in the deciding set against Australia's Ajla Tomljanovic.

But that ill-discipline appeared a distant memory on Friday night, the two-time grand slam champion easing through her contest against the 32nd seed in just 79 minutes.

"I felt more confident after the match against Ajla, because when you stay mentally strong during the matches, you get an extra boost the next one," said Halep, who added that a shoulder problem she'd been carrying settled down in the match.

Looking more like the player that peeled off five games to get over the line against the Australian than the one who was two points from exiting the slam, the Romanian started in commanding fashion.

She reeled off a similar run to go from 1-1 in the opening set against the Russian to have it in the bank after 31 minutes.

Things got a little more complicated in the second.

The 2018 Australian Open runner-up found herself down a break at 3-2 only to strike straight back after some of her trademark defence kept her in the game.

She then won the next three games to close out the match.

"I've had tough matches, but I'm really happy that after the third one I feel much better, the game also and the body," Halep said.

"You know, first week is like what Pete Sampras used to say, it's about surviving because you cannot win the grand slam in the first week."

Kudermetova, who had been in excellent early-season form with a run through to the Abu Dhabi final just last month, hard pushed much harder in the second set but was often let down by her first serve which finished at just 42 per cent.

She does however exit with her equal-best grand slam showing.

Halep will now play the winner of the late match between defending French Open champion Iga Swiatek and France's Fiona Ferro.

Australian Associated Press