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Dart had made a fine start to the match against the Japanese world No 82, winning the first two games, but suffered an alarming loss of momentum, losing the next eight games.
She refused to give up however, turning a 2-0 deficit in the second set into a 6-4 triumph and was the pace maker for much of the third set, twice moving a break ahead, only to lose her lead, the second time after squandering two match points.
In the ensuring match tiebreaker, she had trailed 5-1 but won nine of the next 10 points to record her first-ever win at Melbourne Park, following her impressive run to the Wimbledon third round last year.
Australian Open Highlights - Thriller as Harriet Dart takes on Misaki Doi
"Being able to keep my composure at big moments," she said when asked by Eurosport about what encouraged her about her performance. "I'm really proud of myself for that. I was just relieved to get the win in the end."
And the reward is a clash against Halep, a finalist here two years ago who has two Grand Slam titles under her belt, most likely to take place on a show court, and she is keen to learn having been dispatched 6-1, 6-1 by Ashleigh Barty on Centre Court at Wimbledon last year.
Harriet Dart: I’ll take my game to Simona Halep
"She's an incredible champion, it's going to be a very tough match. It's another great opportunity to see where my game's at and take my game to her.
"I hope [I can shine on a show court]. I think over the last year I've learned from playing in some big opportunities, big matches on big courts, hopefully I can use that experience and take it with me into the next match."
Harriet Dart 'proud of herself' after first career win at Australian Open
Halep was less than fluent herself in the first set of her 7-6, 6-1 win over Jennifer Brady, taking a nasty fall in the first set which saw her receive treatment to her wrist.
If Dart can arrest the long runs of lost points and games which plagued her progress against Doi and show some of the grit she did to come back from seemingly impossible positions, she may walk away from her match with Halep very satisfied, with considerable progress in her career having been made.