Crowd favourite and third seed Halep coped with gusty conditions at the Aviation Club as she beat Lesia Tsurenko 6-3, 7-5, breaking seven times. Could the current world No8 make it a hat-trick in the desert, after the disappointment of letting a 4-1 lead slip in her three-set loss to Halep in Doha last week?
Elsewhere, Hsieh Su-Wei defeated Belarusian Aliaksandra Sasnovich 6-1, 6-2 while Viktoria Kuzmova accounted for seventh seed Kiki Bertens, beating this month's St Petersburg champion 6-2, 4-6, 7-6 (8/6).
"I don't think I necessarily understand what position I'm in in a way", Osaka said of her struggle to come to terms with the fact that she is one of the highest profile stars in tennis right now.
Hsieh, who has also beaten top players like Simona Halep and Garbine Muguruza in the past, says she will continue to fight hard for good results. Taiwan's Hsieh Su-Wei in action during the match against Japan's Naomi Osaka. "It didn't feel like last week", Halep said.
Following her victory at the Australian Open, she arrived in Dubai with the unexpected news that she had split with her coach Sascha Bajin after her Melbourne title run.
But the player bounced back all guns blazing in the match that lasted for two hours and 34 minutes. "I tried to finish the points faster because I'm a little bit exhausted", Halep said. I'm more relaxed. I don't put pressure on myself. I feel good on court. "I'm confident. I feel good on court even if I'm exhausted".
The Romanian will play her quarter-final against a charged-up Belinda Bencic, who saved seven match points before converting the first of her own to beat Aryna Sabalenka 6-4, 2-6, 7-6 (9/7).
It was at this point that Osaka briefly broke down and had to hide her face as she wiped away tears.
The Spaniard edged past Kristina Mladenovic, surprise conqueror of world number one Naomi Osaka, sending the Dubai-based Frenchwoman out 7-5, 7-5. Alison Risk of the United States also advanced with a 6-2, 6-3 win over France's Alizé Cornet 6-2, 6-3.
"I have no idea how I won, I was thinking many times during the match points that I was already back in the locker room", said Bencic.
"It means a lot, honestly", Mladenovic said after booking a match with a Spain's Carla Suarez Navarro in the last 16.