Kvitova, the 2013 winner, recovered from losing a first-set tiebreak to defeat Katerina Siniakova 6-7 (3/7), 6-4, 6-4 and squeeze into the third round.
Halep, Dubai champion in 2015, beat 2014 Wimbledon finalist Eugenie Bouchard 7-6 (7/4), 6-4.
The Romanian said she is still feeling the effects of her weekend final defeat in Doha by Elise Mertens.
"It was a good match because I won it. I tried to finish the points faster because I'm a little bit tired," Halep said.
"She played well, the level was pretty good. At some points I really ran very well. I'm confident. I feel good on court even if I'm tired."
A third former world number one also advanced as Angelique Kerber beat Dalila Jakupovic 7-6 (7/4), 6-3.
Kvitova, Wimbledon champion in 2011 and 2014, said she was unfazed about the early midday start to her match.
"I don't really care if I play the first match," the Australian Open runner-up said. "Now I'm done, so I have a free afternoon.
"I'm not sure what I'm pleased with... maybe with my comeback at the end.
"Even when I lost the tie-break, I was really fighting in the first set to get it done, then the tie-break was just a little bad from my side.
"I won my first two games in the second set. It was really helpful for me mentally. That's probably what I'm pleased with."