Halep, playing in her first tournament since a back injury cut short her 2018 season, lost 6-4 6-4 in 87 minutes with the result dealing a blow to her Australian Open preparations.
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Australian Barty, who is ranked 15th in the world, fired 26 winners and won four out of seven break points as she recorded her first victory over a reigning world number one.
The 22-year-old Barty will play 10th seed Elise Mertens in the quarter-finals following the Belgian's 6-3 6-1 win over Estonian Anett Kontaveit.
Earlier on Wednesday, Mertens won 7-6 (4) 2-6 6-2 in her first-round match with Katerina Siniakova, while Kontaveit beat Monica Puig 2-6 7-5 6-1.
In the bottom half of the draw, defending champion Angelique Kerber faces a mouthwatering last-eight encounter against two-time Wimbledon champion Petra Kvitova.
Czech Kvitova, who won this tournament in 2015, battled past Su-wei Hsieh 7-6 (2) 6-2, with three-time grand slam champion Kerber already having beaten Italy’s Giorgi Camila in straight sets on Tuesday.
Fourth seed Sloane Stephens was knocked out by qualifier Yulia Putintseva after surrendering a one-set lead to lose 3-6 7-6 (4) 6-0.
Kiki Bertenes, seeded seventh, awaits Putintseva after she received a walkover win due to former world number one Garbine Muguruza suffering a gastrointestinal illness.
The other quarter-final will see qualifier Aliaksandra Sasnovich play Switzerland’s Timea Bacsinszky.
Belarusian Sasnovich defeated Priscilla Hon 0-6 6-3 6-3, while Bacsinszky also came from a set down to beat an Australian player, winning 5-7 6-4 6-3 against Sam Stosur.
At the Hobart International, France’s Alize Cornet remains on course to regain the title she won in 2016 after easing into the quarter-finals.
The sixth seed beat compatriot Pauline Parmentier 6-3 6-0 to set up a meeting with Belgian qualifier Greet Minnen, a 6-1 4-6 7-6 (3) winner against Magda Linette.
Seventh seed Kirsten Flipkens came from a set down to win 6-7 (3) 6-4 6-1 against Viktoria Kuzmova.
Unseeded American Sofia Kenin will be her last-eight opponent following her 7-6 (6) 6-3 success against Tunisian Ons Jabeur.
Elsewhere, Anna Karolina Schmiedlova beat eighth seed Alison van Uytvanck 6-3 6-2 and Irina-Camelia Begu defeated Anna Blinkova 4-6 7-6 (2) 6-2.
In Wednesday’s other matches, Belinda Bencic comfortably overcame Zoe Hives 6-2 6-4, while Dayana Yastremska claimed a 6-1 6-4 victory over Vera Lapko.
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