MELBOURNE, Australia - There was no stunning defeat for Simona Halep at the Australian Open on Tuesday night against one of the game's most dangerous floaters.

In a rematch of an opening-round upset from the last Grand Slam of 2018, the World No.1 rallied from a set down to defeat Estonian No.2 Kaia Kanepi, 6-7(2), 6-4, 6-2, to book her spot in the second round in Melbourne.

The former Top 15 Estonian knocked the Romanian out of the US Open in the first round last summer in an Open Era first, but the Romanian dug deep to prevent a repeat inside Margaret Court Arena in her first Grand Slam match of 2019.

Their previous meeting was at the back of Halep's mind coming in - "It was a bit of pressure on my shoulders," she admitted. But it also relaxed her. "I have nothing to lose," she smiled. 

"I know that she's hitting the ball very strong, is going to take time to get the lead in the match. I didn't give up, which was really important tonight."

Trailing by a set and a break after losing serve in the third game of the second set, Halep responded by breaking back immeditely and never lost serve for the rest of the match.

Both players entered the match under somewhat of an injury cloud: Halep was seeking her first win since August in just her second tournament appearance thanks to a back injury, while Kanepi was playing her first match since another run to the second week at Flushing Meadows.

Again, though, Halep turned this negative into a positive. Declaring that she has "no expectations" this week, the27-year-old's goals are both more specific and more general. On a micro level, she said, she is "just giving my best to find the rhythm... I feel like I am one step forward."

But on a macro level, Halep is learning to approach the game in a different way. "I'm trying just to enjoy more and to be happy on court," she explained. "So nothing else. The results don't matter any more. I just want to improve in myself and also in my game. Everything I do, I do for this."

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Kanepi hammered 40 winners as she sought the upset bid, and a third career win against a reigning World No.1, but was undone by over 60 unforced errors over two hours and 11 minutes.

She nonetheless stayed in touch in the final set, as neither woman faced a break point over the first five games of the decider, but last year's runner-up Halep raised her level over the match's final stages.

The top seed won the final four games to avoid the upset, and advance to a second-round meeting against another dangerous floater: last week's Hobart International champion Sofia Kenin.