Marin Cilic overcame a pair of match points - including one double-faulted away by Fernando Verdasco - and a two-set deficit for a 4-6, 3-6, 6-1, 7-6 (8), 6-3 victory in the Australian Open's third round.
The veteran has reached the final at Melbourne Park twice, most recently in 2017 when she lost to sister Serena.
The Romanian top seed, set up a mouth-watering clash with seven-time Grand Slam champion Venus Williams.
"It is always hard to play Kaia", said Halep, who raged in frustration at her support team at times before finally taking control of the match in the third set.
But self-assured Svitolina is bubbling with confidence after dismantling Viktoria Kuzmova 6-4, 6-1, while Pliskova woke up after losing the first set to race past Madison Brengle 4-6, 6-1, 6-0. And the victor of that could face Williams' younger sister, 23-time major champ Serena, in the fourth round. That broke the resistance of her opponent and Williams eased to a 6-2 win in the final set.
Williams is in Australia aiming for a 24th Grand Slam singles title. The 20-year-old won it seven points to five.
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Williams, 37, will next play Dayana Yastremska, who beat No. 23 Carla Suarez Navarro 6-3, 3-6, 6-1. But it was another three-set affair that she faced in the second round.
I do not know I how won. Her only win previously came against Svitolina in Australia a year ago.
Earlier, 2016 US Open finalist Karolina Pliskova extended her winning start to the season after a rain-interrupted 4-6, 6-1, 6-0 win over Madison Brengle.
Birrell said she anticipated a few more friends from the Gold Coast joining her entourage before then.
Halep was absolutely cruising at one set up and a break up in the second set. "Hopefully in the next round, I'll play better and make a better match". The next highest seed in Djokovic's half, No. 4 Alexander Zverev, plays Australian wild-card entry Alex Bolt, who beat No. 29 Gilles Simon in the second round.