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|Ukraine's Elina Svitolina returns the ball to Spain's Garbine Muguruza during the Dubai Championships. (Source: AP Photo/Kamran Jebreili)|
Second seed Kvitova outlasted American qualifier Jennifer Brady 7-5, 1-6, 6-3.
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.
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).
"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.
"I have nothing to lose against Halep, she's a great player. But I have gained energy from this win."
Tsurenko managed just a single point over the last three games as former world number one Halep demonstrated her superiority by taking a 7-0 lead in their head-to-head record.
Svitolina put on the most dominant performance, crushing former Wimbledon and Roland Garros champion Garbine Muguruza 6-1, 6-2 in just 62 minutes.
She is bidding to become the first woman to win the tournament three times and next faces Carla Suarez Navarro.
The Spaniard edged past Kristina Mladenovic, surprise conqueror of world number one Naomi Osaka, sending the Dubai-based Frenchwoman out 7-5, 7-5.
Suarez Navarro started on the back foot but rallied to overcome a 5-1 deficit in the first set on the way to victory.
But she was not impressed with her own effort.
"I didn't play good today. I started badly," the world number 26 said. "Sometimes is not easy take the confidence back again."
PLISKOVA BATTLES PAST RISKE
Fourth-seeded Karolina Pliskova was tested by Alison Riske, with the Czech taking more than two hours to produce a 7-6 (7/3), 7-6 (7/5) victory.
The 2015 finalist won a marathon game late in the second set, holding for 5-5 after seven deuces plus two set points for her American opponent.
Pliskova broke a game later but dropped serve herself to force a tie-breaker; the decider ended on a first match point after Riske double-faulted.
Angelique Kerber, a semi-finalist on her last two appearances here, lost to Hsieh Su-Wei 5-7, 6-4, 6-0.
Meanwhile, Kvitova, who won the Dubai trophy in 2013, had not played on the WTA Tour since reaching the St Petersburg quarter-finals a fortnight ago.
"When I came here, I didn't really have many days of practice, to be honest," the two-time Wimbledon winner said.
"I had something different to do in my life. I wasn't really that prepared for this tournament.
"But I'm happy I was able to get two wins. It's great when you're not playing your best and you still find a way to win."
Halep, a finalist in Doha last week, was supported even in the middle of a workday by scores of chanting, enthusiastic local Romanian fans, and her country's ambassador to the UAE, as she saw off Tsurenko in tricky conditions.
"The wind was difficult today. It didn't feel like last week," Halep said. "I know how she's playing, it's not my favourite style because she doesn't give any power (on the ball).
"I've had many matches with her and won them. I feel confident when I play her."
Third round results:
Petra Kvitova (CZE) bt Jennifer Brady (USA) 7-5, 1-6, 6-3
Simona Halep (ROM) bt Lesia Tsurenko (UKR) 6-3, 7-5
Viktoria Kuzmova (SVK) bt Sofia Kenin (USA) 1-6, 7-5, 6-2
Hsieh Su-Wei (TPE) bt Angelique Kerber (GER) 5-7, 6-4, 6-0
Karolina Pliskova (CZE) bt Alison Riske (USA) 7-6 (7/3), 7-6 (7/5)
Carla Suarez Navarro (ESP) bt Kristina Mladenovic (FRA) 7-5, 7-5
Elina Svitolina (UKR) bt Garbine Muguruza (ESP) 6-1, 6-2
Belinda Bencic (SUI) bt Aryna Sabalenka (BLR) 6-4, 2-6, 7-6 (9/7)